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| basic linear algebra subprograms: High Performance Computing for Computational Science -- VECPAR 2010 José M. Laginha M. Palma, Michel Daydé, Osni Marques, Joao Correia Lopes, 2011-02-23 This book constitutes the thoroughly refereed post-conference proceedings of the 9th International Conference on High Performance Computing for Computational Science, VECPAR 2010, held in Berkeley, CA, USA, in June 2010. The 34 revised full papers presented together with five invited contributions were carefully selected during two rounds of reviewing and revision. The papers are organized in topical sections on linear algebra and solvers on emerging architectures, large-scale simulations, parallel and distributed computing, numerical algorithms. |
| basic linear algebra subprograms: LAPACK Users' Guide E. Anderson, Z. Bai, C. Bischof, S. Blackford, J. Dongarra, J. Du Croz, A. Greenbaum, S. Hammarling, A. McKenney, D. Sorensen, 1999-01-01 LAPACK is a library of numerical linear algebra subroutines designed for high performance on workstations, vector computers, and shared memory multiprocessors. Release 3.0 of LAPACK introduces new routines and extends the functionality of existing routines. |
| basic linear algebra subprograms: Solving Least Squares Problems Charles L. Lawson, Richard J. Hanson, 1995-12-01 This Classic edition includes a new appendix which summarizes the major developments since the book was originally published in 1974. The additions are organized in short sections associated with each chapter. An additional 230 references have been added, bringing the bibliography to over 400 entries. Appendix C has been edited to reflect changes in the associated software package and software distribution method. |
| basic linear algebra subprograms: Using PLAPACK--parallel Linear Algebra Package Robert A. Van de Geijn, 1997 This book is a comprehensive introduction to all the components of a high-performance parallel linear algebra library, as well as a guide to the PLAPACK infrastructure. PLAPACK is a library infrastructure for the parallel implementation of linear algebra algorithms and applications on distributed memory supercomputers such as the Intel Paragon, IBM SP2, Cray T3D/T3E, SGI PowerChallenge, and Convex Exemplar. This infrastructure allows library developers, scientists, and engineers to exploit a natural approach to encoding so-called blocked algorithms, which achieve high performance by operating on submatrices and subvectors. This feature, as well as the use of an alternative, more application-centric approach to data distribution, sets PLAPACK apart from other parallel linear algebra libraries, allowing for strong performance and significanltly less programming by the user. This book is a comprehensive introduction to all the components of a high-performance parallel linear algebra library, as well as a guide to the PLAPACK infrastructure. Scientific and Engineering Computation series |
| basic linear algebra subprograms: ScaLAPACK User's Guide L. S. Blackford, 1997 Accompanying CD-ROM includes HTML version of the ScaLAPACK User's Guide, the source code for the package, testing and timing programs, prebuilt versions of the library for a number of computers, example programs, and the full set of LAPACK working notes. |
| basic linear algebra subprograms: Introduction to Computational Linear Algebra Nabil Nassif, Jocelyne Erhel, Bernard Philippe, 2015-06-24 Teach Your Students Both the Mathematics of Numerical Methods and the Art of Computer ProgrammingIntroduction to Computational Linear Algebra presents classroom-tested material on computational linear algebra and its application to numerical solutions of partial and ordinary differential equations. The book is designed for senior undergraduate stud |
| basic linear algebra subprograms: Graph Algorithms in the Language of Linear Algebra Jeremy Kepner, John Gilbert, 2011-01-01 The current exponential growth in graph data has forced a shift to parallel computing for executing graph algorithms. Implementing parallel graph algorithms and achieving good parallel performance have proven difficult. This book addresses these challenges by exploiting the well-known duality between a canonical representation of graphs as abstract collections of vertices and edges and a sparse adjacency matrix representation. This linear algebraic approach is widely accessible to scientists and engineers who may not be formally trained in computer science. The authors show how to leverage existing parallel matrix computation techniques and the large amount of software infrastructure that exists for these computations to implement efficient and scalable parallel graph algorithms. The benefits of this approach are reduced algorithmic complexity, ease of implementation, and improved performance. |
| basic linear algebra subprograms: LINPACK Users' Guide J. J. Dongarra, J. R. Bunch, C. B. Moler, G. W. Stewart, 1979-01-01 The authors of this carefully structured guide are the principal developers of LINPACK, a unique package of Fortran subroutines for analyzing and solving various systems of simultaneous linear algebraic equations and linear least squares problems. This guide supports both the casual user of LINPACK who simply requires a library subroutine, and the specialist who wishes to modify or extend the code to handle special problems. It is also recommended for classroom work. |
| basic linear algebra subprograms: Handbook of Linear Algebra Leslie Hogben, 2013-11-26 With a substantial amount of new material, the Handbook of Linear Algebra, Second Edition provides comprehensive coverage of linear algebra concepts, applications, and computational software packages in an easy-to-use format. It guides you from the very elementary aspects of the subject to the frontiers of current research. Along with revisions and |
| basic linear algebra subprograms: Matrix Computations Gene Howard Golub, Charles F. Van Loan, 1983 |
| basic linear algebra subprograms: Introduction to Linear Algebra Gilbert Strang, 2016-08-11 Linear algebra is something all mathematics undergraduates and many other students, in subjects ranging from engineering to economics, have to learn. The fifth edition of this hugely successful textbook retains all the qualities of earlier editions, while at the same time seeing numerous minor improvements and major additions. The latter include: • A new chapter on singular values and singular vectors, including ways to analyze a matrix of data • A revised chapter on computing in linear algebra, with professional-level algorithms and code that can be downloaded for a variety of languages • A new section on linear algebra and cryptography • A new chapter on linear algebra in probability and statistics. A dedicated and active website also offers solutions to exercises as well as new exercises from many different sources (including practice problems, exams, and development of textbook examples), plus codes in MATLAB®, Julia, and Python. |
| basic linear algebra subprograms: Computing in Object-Oriented Parallel Environments Denis Caromel, Rodney R. Oldehoeft, Marydell Tholburn, 1998-11-25 This volume contains the Proceedings of the International Symposium on C- puting in Object-Oriented Parallel Environments (ISCOPE ’98), held at Santa 1 Fe, New Mexico, USA on December 8{11, 1998. ISCOPE is in its second year, and continues to grow both in attendance and in the diversity of the subjects covered. ISCOPE’97 and its predecessor conferences focused more narrowly on scienti c computing in the high-performance arena. ISCOPE ’98 retains this emphasis, but has broadened to include discrete-event simulation, mobile c- puting, and web-based metacomputing. The ISCOPE ’98 Program Committee received 39 submissions, and acc- ted 10 (26%) as Regular Papers, based on their excellent content, maturity of development, and likelihood for widespread interest. These 10 are divided into three technical categories. Applications: The rst paper describes an approach to simulating advanced nuclear power reactor designs that incorporates multiple local solution - thods and a natural extension to parallel execution. The second paper disc- ses a Time Warp simulation kernel that is highly con gurable and portable. The third gives an account of the development of software for simulating high-intensity charged particle beams in linear particle accelerators, based on the POOMA framework, that shows performance considerably better than an HPF version, along with good parallel speedup. |
| basic linear algebra subprograms: LAPACK95 Users' Guide V. A. Barker, L. S. Blackford, J. Dongarra, J. Du Croz, S. Hammarling, M. Marinova, J. Wa?niewski, P. Yalamov, 2001-01-01 LAPACK95 Users' Guide provides an introduction to the design of the LAPACK95 package. |
| basic linear algebra subprograms: The Art of Differentiating Computer Programs Uwe Naumann, 2012-01-01 This is the first entry-level book on algorithmic (also known as automatic) differentiation (AD), providing fundamental rules for the generation of first- and higher-order tangent-linear and adjoint code. The author covers the mathematical underpinnings as well as how to apply these observations to real-world numerical simulation programs. Readers will find: examples and exercises, including hints to solutions; the prototype AD tools dco and dcc for use with the examples and exercises; first- and higher-order tangent-linear and adjoint modes for a limited subset of C/C++, provided by the derivative code compiler dcc; a supplementary website containing sources of all software discussed in the book, additional exercises and comments on their solutions (growing over the coming years), links to other sites on AD, and errata. |
| basic linear algebra subprograms: Matrix Computations Gene H. Golub, Charles F. Van Loan, 1996-10-15 Revised and updated, the third edition of Golub and Van Loan's classic text in computer science provides essential information about the mathematical background and algorithmic skills required for the production of numerical software. This new edition includes thoroughly revised chapters on matrix multiplication problems and parallel matrix computations, expanded treatment of CS decomposition, an updated overview of floating point arithmetic, a more accurate rendition of the modified Gram-Schmidt process, and new material devoted to GMRES, QMR, and other methods designed to handle the sparse unsymmetric linear system problem. |
| basic linear algebra subprograms: Handbook for Matrix Computations Thomas F. Coleman, Charles Van Loan, 1988-01-01 Mathematics of Computing -- Numerical Analysis. |
| basic linear algebra subprograms: Linear Algebra Ward Cheney, David Kincaid, 2012 Ward Cheney and David Kincaid have developed Linear Algebra: Theory and Applications, Second Edition, a multi-faceted introductory textbook, which was motivated by their desire for a single text that meets the various requirements for differing courses within linear algebra. For theoretically-oriented students, the text guides them as they devise proofs and deal with abstractions by focusing on a comprehensive blend between theory and applications. For application-oriented science and engineering students, it contains numerous exercises that help them focus on understanding and learning not only vector spaces, matrices, and linear transformations, but uses of software tools available for use in applied linear algebra. Using a flexible design, it is an ideal textbook for instructors who wish to make their own choice regarding what material to emphasis, and to accentuate those choices with homework assignments from a large variety of exercises, both in the text and online. |
| basic linear algebra subprograms: Accuracy and Stability of Numerical Algorithms Nicholas J. Higham, 2002-01-01 Accuracy and Stability of Numerical Algorithms gives a thorough, up-to-date treatment of the behavior of numerical algorithms in finite precision arithmetic. It combines algorithmic derivations, perturbation theory, and rounding error analysis, all enlivened by historical perspective and informative quotations. This second edition expands and updates the coverage of the first edition (1996) and includes numerous improvements to the original material. Two new chapters treat symmetric indefinite systems and skew-symmetric systems, and nonlinear systems and Newton's method. Twelve new sections include coverage of additional error bounds for Gaussian elimination, rank revealing LU factorizations, weighted and constrained least squares problems, and the fused multiply-add operation found on some modern computer architectures. |
| basic linear algebra subprograms: ScaLAPACK Users' Guide L. S. Blackford, 1997-01-01 ScaLAPACK is an acronym for Scalable Linear Algebra Package or Scalable LAPACK. It is a library of high-performance linear algebra routines for distributed memory message-passing MIMD computers and networks of workstations supporting parallel virtual machine (PVM) and/or message passing interface (MPI). It is a continuation of the LAPACK project, which designed and produced analogous software for workstations, vector supercomputers, and shared memory parallel computers. Both libraries contain routines for solving systems of linear equations, least squares problems, and eigenvalue problems. The goals of both projects are efficiency, scalability, reliability, portability, flexibility, and ease of use. ScaLAPACK includes routines for the solution of dense, band, and tridiagonal linear systems of equations, condition estimation and iterative refinement, for LU and Cholesky factorization, matrix inversion, full-rank linear least squares problems, orthogonal and generalized orthogonal factorizations, orthogonal transformation routines, reductions to upper Hessenberg, bidiagonal and tridiagonal form, reduction of a symmetric-definite/ Hermitian-definite generalized eigenproblem to standard form, the symmetric/Hermitian, generalized symmetric/Hermitian, and nonsymmetric eigenproblem, and the singular value decomposition. Prototype codes are provided for out-of-core linear solvers for LU, Cholesky, and QR, the matrix sign function for eigenproblems, an HPF interface to a subset of ScaLAPACK routines, and SuperLU. Software is available in single-precision real, double-precision real, single-precision complex, and double-precision complex. The software has been written to be portable across a wide range of distributed-memory environments such as the Cray T3, IBM SP, Intel series, TM CM-5, networks of workstations, and any system for which PVM or MPI is available. Each Users' Guide includes a CD-ROM containing the HTML version of the ScaLAPACK Users' Guide, the source code for ScaLAPACK and LAPACK, testing and timing programs, prebuilt versions of the library for a number of computers, example programs, and the full set of LAPACK Working Notes. |
| basic linear algebra subprograms: Matrix Algebra James E. Gentle, 2007-08-06 Matrix algebra is one of the most important areas of mathematics for data analysis and for statistical theory. This much-needed work presents the relevant aspects of the theory of matrix algebra for applications in statistics. It moves on to consider the various types of matrices encountered in statistics, such as projection matrices and positive definite matrices, and describes the special properties of those matrices. Finally, it covers numerical linear algebra, beginning with a discussion of the basics of numerical computations, and following up with accurate and efficient algorithms for factoring matrices, solving linear systems of equations, and extracting eigenvalues and eigenvectors. |
| basic linear algebra subprograms: Supercomputing Frontiers Rio Yokota, Weigang Wu, 2018-03-20 It constitutes the refereed proceedings of the 4th Asian Supercomputing Conference, SCFA 2018, held in Singapore in March 2018. Supercomputing Frontiers will be rebranded as Supercomputing Frontiers Asia (SCFA), which serves as the technical programme for SCA18. The technical programme for SCA18 consists of four tracks: Application, Algorithms & Libraries Programming System Software Architecture, Network/Communications & Management Data, Storage & Visualisation The 20 papers presented in this volume were carefully reviewed nd selected from 60 submissions. |
| basic linear algebra subprograms: Matrix Algorithms G. W. Stewart, 1998-08-01 This volume is the first in a self-contained five-volume series devoted to matrix algorithms. It focuses on the computation of matrix decompositions--that is, the factorization of matrices into products of similar ones. The first two chapters provide the required background from mathematics and computer science needed to work effectively in matrix computations. The remaining chapters are devoted to the LU and QR decompositions--their computation and applications. The singular value decomposition is also treated, although algorithms for its computation will appear in the second volume of the series. The present volume contains 65 algorithms formally presented in pseudocode. Other volumes in the series will treat eigensystems, iterative methods, sparse matrices, and structured problems. The series is aimed at the nonspecialist who needs more than black-box proficiency with matrix computations. To give the series focus, the emphasis is on algorithms, their derivation, and their analysis. The reader is assumed to have a knowledge of elementary analysis and linear algebra and a reasonable amount of programming experience, typically that of the beginning graduate engineer or the undergraduate in an honors program. Strictly speaking, the individual volumes are not textbooks, although they are intended to teach, the guiding principle being that if something is worth explaining, it is worth explaining fully. This has necessarily restricted the scope of the series, but the selection of topics should give the reader a sound basis for further study. |
| basic linear algebra subprograms: Developing Linear Algebra Codes on Modern Processors: Emerging Research and Opportunities Catalán Pallarés, Sandra, Valero-Lara, Pedro, Toledo Díaz, Leonel Antonio, Carratalá Sáez, Rocío, 2022-10-14 Optimized linear algebra (LA) libraries that are able to exploit the underlying hardware are always of interest in the high-performance computing community. The implementation of LA software has evolved along with computer architecture, while the specification remains unaltered almost from the beginning. It is important to differentiate between the specification of LA libraries and their implementation. Because LA libraries pursue high performance, the implementation for a given architecture needs to be optimized for it specifically. However, the type of operations included in the libraries, the input/output parameters, and the data types to be handled are common to all of them. This is why, while the specification remains constant, the implementation evolves with the creation of new architectures. Developing Linear Algebra Codes on Modern Processors: Emerging Research and Opportunities presents the main characteristics of LA libraries, showing the differences between the standards for sparse and dense versions. It further explores relevant linear algebra problems and shows, in a clear and understandable way, how to solve them using different computer architectures. Covering topics such as programming models, batched computing, and distributed memory platforms, this premier reference source is an excellent resource for programmers, computer scientists, engineers, students and faculty of higher education, librarians, researchers, and academicians. |
| basic linear algebra subprograms: A Journey through the History of Numerical Linear Algebra Claude Brezinski , Gérard Meurant , Michela Redivo-Zaglia, 2022-12-06 This expansive volume describes the history of numerical methods proposed for solving linear algebra problems, from antiquity to the present day. The authors focus on methods for linear systems of equations and eigenvalue problems and describe the interplay between numerical methods and the computing tools available at the time. The second part of the book consists of 78 biographies of important contributors to the field. A Journey through the History of Numerical Linear Algebra will be of special interest to applied mathematicians, especially researchers in numerical linear algebra, people involved in scientific computing, and historians of mathematics. |
| basic linear algebra subprograms: Matrix Analysis and Computations Zhong-Zhi Bai, Jian-Yu Pan, 2021-09-09 This comprehensive book is presented in two parts; the first part introduces the basics of matrix analysis necessary for matrix computations, and the second part presents representative methods and the corresponding theories in matrix computations. Among the key features of the book are the extensive exercises at the end of each chapter. Matrix Analysis and Computations provides readers with the matrix theory necessary for matrix computations, especially for direct and iterative methods for solving systems of linear equations. It includes systematic methods and rigorous theory on matrix splitting iteration methods and Krylov subspace iteration methods, as well as current results on preconditioning and iterative methods for solving standard and generalized saddle-point linear systems. This book can be used as a textbook for graduate students as well as a self-study tool and reference for researchers and engineers interested in matrix analysis and matrix computations. It is appropriate for courses in numerical analysis, numerical optimization, data science, and approximation theory, among other topics |
| basic linear algebra subprograms: Introduction to Parallel Computing Wesley Petersen, Peter Arbenz, 2004-01-08 In the last few years, courses on parallel computation have been developed and offered in many institutions in the UK, Europe and US as a recognition of the growing significance of this topic in mathematics and computer science. There is a clear need for texts that meet the needs of students and lecturers and this book, based on the author's lecture at ETH Zurich, is an ideal practical student guide to scientific computing on parallel computers working up from a hardware instruction level, to shared memory machines, and finally to distributed memory machines. Aimed at advanced undergraduate and graduate students in applied mathematics, computer science, and engineering, subjects covered include linear algebra, fast Fourier transform, and Monte-Carlo simulations, including examples in C and, in some cases, Fortran. This book is also ideal for practitioners and programmers. |
| basic linear algebra subprograms: Handbook of Parallel Computing and Statistics Erricos John Kontoghiorghes, 2005-12-21 Technological improvements continue to push back the frontier of processor speed in modern computers. Unfortunately, the computational intensity demanded by modern research problems grows even faster. Parallel computing has emerged as the most successful bridge to this computational gap, and many popular solutions have emerged based on its concepts |
| basic linear algebra subprograms: High Performance Computing for Computational Science - VECPAR 2002 José M.L.M. Palma, 2003-04-07 This book constitutes the thoroughly refereed post-proceedings of the 5th International Conference on High Performance Computing for Computational Science, VECPAR 2002, held in Porto, Portugal in June 2002. The 45 revised full papers presented together with 4 invited papers were carefully selected during two rounds of reviewing and improvement. The papers are organized in topical sections on fluids and structures, data mining, computing in chemistry and biology, problem solving environments, computational linear and non-linear algebra, cluster computing, imaging, and software tools and environments. |
| basic linear algebra subprograms: Numerical Linear Algebra for Applications in Statistics James E. Gentle, 2012-12-06 Accurate and efficient computer algorithms for factoring matrices, solving linear systems of equations, and extracting eigenvalues and eigenvectors. Regardless of the software system used, the book describes and gives examples of the use of modern computer software for numerical linear algebra. It begins with a discussion of the basics of numerical computations, and then describes the relevant properties of matrix inverses, factorisations, matrix and vector norms, and other topics in linear algebra. The book is essentially self- contained, with the topics addressed constituting the essential material for an introductory course in statistical computing. Numerous exercises allow the text to be used for a first course in statistical computing or as supplementary text for various courses that emphasise computations. |
| basic linear algebra subprograms: Encyclopedia of Parallel Computing David Padua, 2014-07-08 Containing over 300 entries in an A-Z format, the Encyclopedia of Parallel Computing provides easy, intuitive access to relevant information for professionals and researchers seeking access to any aspect within the broad field of parallel computing. Topics for this comprehensive reference were selected, written, and peer-reviewed by an international pool of distinguished researchers in the field. The Encyclopedia is broad in scope, covering machine organization, programming languages, algorithms, and applications. Within each area, concepts, designs, and specific implementations are presented. The highly-structured essays in this work comprise synonyms, a definition and discussion of the topic, bibliographies, and links to related literature. Extensive cross-references to other entries within the Encyclopedia support efficient, user-friendly searchers for immediate access to useful information. Key concepts presented in the Encyclopedia of Parallel Computing include; laws and metrics; specific numerical and non-numerical algorithms; asynchronous algorithms; libraries of subroutines; benchmark suites; applications; sequential consistency and cache coherency; machine classes such as clusters, shared-memory multiprocessors, special-purpose machines and dataflow machines; specific machines such as Cray supercomputers, IBM’s cell processor and Intel’s multicore machines; race detection and auto parallelization; parallel programming languages, synchronization primitives, collective operations, message passing libraries, checkpointing, and operating systems. Topics covered: Speedup, Efficiency, Isoefficiency, Redundancy, Amdahls law, Computer Architecture Concepts, Parallel Machine Designs, Benmarks, Parallel Programming concepts & design, Algorithms, Parallel applications. This authoritative reference will be published in two formats: print and online. The online edition features hyperlinks to cross-references and to additional significant research. Related Subjects: supercomputing, high-performance computing, distributed computing |
| basic linear algebra subprograms: Applied Parallel Computing. Industrial Computation and Optimization Jerzy Wasniewski, 1996-12-11 Although the last decade has witnessed significant advances in control theory for finite and infinite dimensional systems, the stability and control of time-delay systems have not been fully investigated. Many problems exist in this field that are still unresolved, and there is a tendency for the numerical methods available either to be too general or too specific to be applied accurately across a range of problems. This monograph brings together the latest trends and new results in this field, with the aim of presenting methods covering a large range of techniques. Particular emphasis is placed on methods that can be directly applied to specific problems. The resulting book is one that will be of value to both researchers and practitioners. |
| basic linear algebra subprograms: Applied Parallel Computing. Computations in Physics, Chemistry and Engineering Science Jack Dongarra, Kaj Madsen, Jerzy Wasniewski, 1996-02-27 This book presents the refereed proceedings of the Second International Workshop on Applied Parallel Computing in Physics, Chemistry and Engineering Science, PARA'95, held in Lyngby, Denmark, in August 1995. The 60 revised full papers included have been contributed by physicists, chemists, and engineers, as well as by computer scientists and mathematicians, and document the successful cooperation of different scientific communities in the booming area of computational science and high performance computing. Many widely-used numerical algorithms and their applications on parallel computers are treated in detail. |
| basic linear algebra subprograms: Numerical Analysis and Its Applications Lubin Vulkov, Jerzy Wasniewski, Plamen Yalamov, 2003-07-31 This book constitutes the thoroughly refereed post-proceedings of the Second International Conference on Numerical Analysis and Its Applications, NAA 2000, held in Rousse, Bulgaria in June 2000.The 90 revised papers presented were carefully selected for inclusion in the book during the two rounds of inspection and reviewing. All current aspects of numerical analysis are addressed. Among the application fields covered are computational sciences and engineering, chemistry, physics, economics, simulation, etc. |
| basic linear algebra subprograms: Computing in Object-Oriented Parallel Environments Denis Caromel, Rodney R. Oldehoeft, Marydell Tholburn, 2003-07-31 This volume contains the Proceedings of the International Symposium on C- puting in Object-Oriented Parallel Environments (ISCOPE ’98), held at Santa 1 Fe, New Mexico, USA on December 8{11, 1998. ISCOPE is in its second year, and continues to grow both in attendance and in the diversity of the subjects covered. ISCOPE’97 and its predecessor conferences focused more narrowly on scienti c computing in the high-performance arena. ISCOPE ’98 retains this emphasis, but has broadened to include discrete-event simulation, mobile c- puting, and web-based metacomputing. The ISCOPE ’98 Program Committee received 39 submissions, and acc- ted 10 (26%) as Regular Papers, based on their excellent content, maturity of development, and likelihood for widespread interest. These 10 are divided into three technical categories. Applications: The rst paper describes an approach to simulating advanced nuclear power reactor designs that incorporates multiple local solution - thods and a natural extension to parallel execution. The second paper disc- ses a Time Warp simulation kernel that is highly con gurable and portable. The third gives an account of the development of software for simulating high-intensity charged particle beams in linear particle accelerators, based on the POOMA framework, that shows performance considerably better than an HPF version, along with good parallel speedup. |
| basic linear algebra subprograms: Templates for the Solution of Linear Systems Richard Barrett, Michael W. Berry, Tony F. Chan, James Demmel, June Donato, Jack Dongarra, Victor Eijkhout, Roldan Pozo, Charles Romine, Henk van der Vorst, 1994-01-01 In this book, which focuses on the use of iterative methods for solving large sparse systems of linear equations, templates are introduced to meet the needs of both the traditional user and the high-performance specialist. Templates, a description of a general algorithm rather than the executable object or source code more commonly found in a conventional software library, offer whatever degree of customization the user may desire. Templates offer three distinct advantages: they are general and reusable; they are not language specific; and they exploit the expertise of both the numerical analyst, who creates a template reflecting in-depth knowledge of a specific numerical technique, and the computational scientist, who then provides value-added capability to the general template description, customizing it for specific needs. For each template that is presented, the authors provide: a mathematical description of the flow of algorithm; discussion of convergence and stopping criteria to use in the iteration; suggestions for applying a method to special matrix types; advice for tuning the template; tips on parallel implementations; and hints as to when and why a method is useful. |
| basic linear algebra subprograms: CONPAR 90 - VAPP IV Helmar Burkhart, 1990-08-30 Parallel architectures are no longer pure research vehicles, as they were some years ago. There are now many commercial systems competing for market segments in scientific computing. The 1990s are likely to become the decade of parallel processing. CONPAR 90 - VAPP IV is the joint successor meeting of two highly successful international conference series in the field of vector and parallel processing. This volume contains the 79 papers presented at the conference. The various topics of the papers include hardware, software and application issues. Some of the session titles best reflect the contents: new models of computation, logic programming, large-grain data flow, interconnection networks, communication issues, reconfigurable and scalable systems, novel architectures and languages, high performance systems and accelerators, performance prediction / analysis / measurement, performance monitoring and debugging, compile-time analysis and restructurers, load balancing, process partitioning and concurrency control, visualization and runtime analysis, parallel linear algebra, architectures for image processing, efficient use of vector computers, transputer tools and applications, array processors, algorithmic studies for hypercube-type systems, systolic arrays and algorithms. The volume gives a comprehensive view of the state of the art in a field of current interest. |
| basic linear algebra subprograms: Computer Science Ricardo Baeza-Yates, U. Manber, 2012-12-06 Introduction. Historical Overview. Databases: Office Information Systems Engineering (J. Palazzo, D. Alcoba) Artificial Intelligence, Logic, and Functional Programming: A HyperIcon Interface to a Blackboard System for Planning Research Projects (P. Charlton, C. Burdorf). Algorithms and Data Structures: Classification of Quadratic Algorithms for Multiplying Polynomials of Small Degree Over Finite Fields (A. Averbuch et al.). Object Oriented Systems: A Graphical Interactive Object Oriented Development System (M. Adar et al.). Distributed Systems: Preserving Distributed Data Coherence Us. |
| basic linear algebra subprograms: Programming Massively Parallel Processors Wen-mei W. Hwu, David B. Kirk, Izzat El Hajj, 2022-05-28 Programming Massively Parallel Processors: A Hands-on Approach shows both students and professionals alike the basic concepts of parallel programming and GPU architecture. Concise, intuitive, and practical, it is based on years of road-testing in the authors' own parallel computing courses. Various techniques for constructing and optimizing parallel programs are explored in detail, while case studies demonstrate the development process, which begins with computational thinking and ends with effective and efficient parallel programs. The new edition includes updated coverage of CUDA, including the newer libraries such as CuDNN. New chapters on frequently used parallel patterns have been added, and case studies have been updated to reflect current industry practices. - Parallel Patterns Introduces new chapters on frequently used parallel patterns (stencil, reduction, sorting) and major improvements to previous chapters (convolution, histogram, sparse matrices, graph traversal, deep learning) - Ampere Includes a new chapter focused on GPU architecture and draws examples from recent architecture generations, including Ampere - Systematic Approach Incorporates major improvements to abstract discussions of problem decomposition strategies and performance considerations, with a new optimization checklist |
| basic linear algebra subprograms: Sage for Undergraduates Gregory V. Bard, 2015-02-16 As the open-source and free competitor to expensive software like MapleTM, Mathematica®, Magma, and MATLAB®, Sage offers anyone with access to a web browser the ability to use cutting-edge mathematical software and display his or her results for others, often with stunning graphics. This book is a gentle introduction to Sage for undergraduate students toward the end of Calculus II (single-variable integral calculus) or higher-level course work such as Multivariate Calculus, Differential Equations, Linear Algebra, or Math Modeling. The book assumes no background in computer science, but the reader who finishes the book will have learned about half of a first semester Computer Science I course, including large parts of the Python programming language. The audience of the book is not only math majors, but also physics, engineering, finance, statistics, chemistry, and computer science majors. |
| basic linear algebra subprograms: Intelligent Decision Technologies Junzo Watada, Toyohide Watanabe, Gloria Phillips-Wren, Robert J. Howlett, Lakhmi C Jain, 2012-05-20 The Intelligent Decision Technologies (IDT) International Conference encourages an interchange of research on intelligent systems and intelligent technologies that enhance or improve decision making. The focus of IDT is interdisciplinary and includes research on all aspects of intelligent decision technologies, from fundamental development to real applications. IDT has the potential to expand their support of decision making in such areas as finance, accounting, marketing, healthcare, medical and diagnostic systems, military decisions, production and operation, networks, traffic management, crisis response, human-machine interfaces, financial and stock market monitoring and prediction, and robotics. Intelligent decision systems implement advances in intelligent agents, fuzzy logic, multi-agent systems, artificial neural networks, and genetic algorithms, among others. Emerging areas of active research include virtual decision environments, social networking, 3D human-machine interfaces, cognitive interfaces, collaborative systems, intelligent web mining, e-commerce, e-learning, e-business, bioinformatics, evolvable systems, virtual humans, and designer drugs. This volume contains papers from the Fourth KES International Symposium on Intelligent Decision Technologies (KES IDT’12), hosted by researchers in Nagoya University and other institutions in Japan. This book contains chapters based on papers selected from a large number of submissions for consideration for the conference from the international community. The volume represents the current leading thought in intelligent decision technologies. |
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excel2021visual basic打开是灰色的怎么办？ - 知乎
如果Excel 2021 中的 Visual Basic 编辑器打开时显示为灰色，可能是由于以下原因之一： 安装问题：确保已正确安装了 Visual Basic for Applications（VBA）组件。 检查 Microsoft Office 安装是否完整，并尝试 …
一文了解Transformer全貌（图解Transformer） - 知乎
Jan 21, 2025 · Transformer整体结构（输入两个单词的例子） 为了能够对Transformer的流程有个大致的了解，我们举一个简单的例子，还是以之前的为例，将法语"Je suis etudiant"翻译成英文。
为什么说以Basic作为入门语言会变成脑残？ - 知乎
Dijkstra说的这个basic是上古时期的basic，参考小霸王上的basic。其中充斥着GOTO，每行必须有行号，行号满了就不能插入，变量命名受限，没有指针和动态内存分配，有很多使其无法胜任 …
base，basic，basis这个三个词怎么区分? - 知乎
Aug 7, 2020 · basic（尤指作为发展的起点）基本的，初步的，如： 6. He doesn't have mastery of the basic skills of reading, writing and communicating. 他还没掌握基本的读写和交流技巧。【 …
为什么10年前风靡一时的Basic系列语言如今已经很少见到了？ - 知乎
BASIC 这个语言派系的发展，成也 VB 败也 VB。 因为 VB 选择的赛道太讨巧（在当时，也就是世纪交汇那阵，属于先进的 PC 端 GUI 编程），导致各种各样不是初学者的专业开发者都来使 …
excel2021visual basic打开是灰色的怎么办？ - 知乎
如果Excel 2021 中的 Visual Basic 编辑器打开时显示为灰色，可能是由于以下原因之一： 安装问题：确保已正确安装了 Visual Basic for Applications（VBA）组件。 检查 Microsoft Office 安 …
一文了解Transformer全貌（图解Transformer） - 知乎
Jan 21, 2025 · Transformer整体结构（输入两个单词的例子） 为了能够对Transformer的流程有个大致的了解，我们举一个简单的例子，还是以之前的为例，将法语"Je suis etudiant"翻译成英 …
为什么叫.NET？它和C#是什么关系？ - 知乎
一门全新的编程语言Visual Basic .Net。 其全面沿袭了Visual Basic的语法，但是只能跑在.Net Framework这个运行时之上。 愿意是吸引庞大的VB开发者，但是实际上是一个除了语法像VB …
打开word时显示microsoft visual basic运行时错误没有注册类怎么 …
前面有答案提到的禁用COM加载项，这个可以一试，但更可能的是中了类似宏病毒的招，感染了启动模板文件，但由于缺少代码需要的引用文件，比如scrrun.dll，代码无法运行于是报错。
个人4盘位NAS，用什么RAID比较合适，为什么？ - 知乎
两盘位basic：存放电影，下载，电脑备份等非重要数据。 可扩展一盘位usb外接（可以用电脑替代，更理想情况是有第二台nas）：使用套件做最重要的数据定期同步或备份，电影种子，basic …
WPS打开时，老是跳出 微软 自定义项安装程序? - 知乎
知乎，中文互联网高质量的问答社区和创作者聚集的原创内容平台，于 2011 年 1 月正式上线，以「让人们更好的分享知识、经验和见解，找到自己的解答」为品牌使命。知乎凭借认真、专业 …
如何origin在一个图中画两条线，比如这种? - 知乎
导入数据到各个列中，全选数据后，点击 Origin 工具栏上的 Plot ——> Basic 2D ——> Line + Symbol 或者 点击 Origin 下边快捷图标 ，如下图所示 Origin 就会自动绘制两条数据线，如下图 …
