Download or read book Symplectic Factorizations and Parallel Iterative Algorithms for Tridiagonal Systems of Equations written by Roberto Bevilacqua and published by . This book was released on 1990 with total page 28 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Iterative Incomplete Factorization Methods written by Valeri? Pavlovich Il?in and published by World Scientific. This book was released on 1992 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to numerical methods for solving sparse linear algebra systems of very large dimension which arise in the implementation of the mesh approximations of the partial differential equations. Incomplete factorization is the basis of the wide class of preconditioning interative processes with acceleration by conjugate gradients or the Chebyshev technique. Different kinds of explicit and implicit algorithms are considered. Theoretical grounds of correctness and estimates of the convergence velocity of iterations are presented. Together with the results of experimental investigations for the typical examples, this book is the first on systematic studying of the incomplete factorization methods.
Download or read book Mathematical Reviews written by and published by . This book was released on 1999 with total page 1244 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Iterative Solution of Symmetric Quasi Definite Linear Systems written by Dominique Orban and published by SIAM. This book was released on 2017-04-07 with total page 101 pages. Available in PDF, EPUB and Kindle. Book excerpt: Numerous applications, including computational optimization and fluid dynamics, give rise to block linear systems of equations said to have the quasi-definite structure. In practical situations, the size or density of those systems can preclude a factorization approach, leaving only iterative methods as the solution technique. Known iterative methods, however, are not specifically designed to take advantage of the quasi-definite structure. This book discusses the connection between quasi-definite systems and linear least-squares problems, the most common and best understood problems in applied mathematics, and explains how quasi-definite systems can be solved using tailored iterative methods for linear least squares (with half as much work!). To encourage researchers and students to use the software, it is provided in MATLAB, Python, and Julia. The authors provide a concise account of the most well-known methods for symmetric systems and least-squares problems, research-level advances in the solution of problems with specific illustrations in optimization and fluid dynamics, and a website that hosts software in three languages.
Download or read book Parallel Tridiagonal Equation Solvers written by Stanford University. Computer Science Department and published by . This book was released on 1974 with total page 48 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Solution of Partial Differential Equations on Vector and Parallel Computers written by James M. Ortega and published by SIAM. This book was released on 1985-09-01 with total page 99 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics of Computing -- Parallelism.
Download or read book Iterative Solution Methods written by Owe Axelsson and published by Cambridge University Press. This book was released on 1996-03-29 with total page 676 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book deals primarily with the numerical solution of linear systems of equations by iterative methods. The first part of the book is intended to serve as a textbook for a numerical linear algebra course. The material assumes the reader has a basic knowledge of linear algebra, such as set theory and matrix algebra, however it is demanding for students who are not afraid of theory. To assist the reader, the more difficult passages have been marked, the definitions for each chapter are collected at the beginning of the chapter, and numerous exercises are included throughout the text. The second part of the book serves as a monograph introducing recent results in the iterative solution of linear systems, mainly using preconditioned conjugate gradient methods. This book should be a valuable resource for students and researchers alike wishing to learn more about iterative methods.
Download or read book Iterative Methods for Sparse Linear Systems written by Y. Saad and published by Cambridge University Press. This book was released on 2003-04 with total page 554 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics of Computing -- General.
Download or read book Advances On Computer Mathematics And Its Applications written by Elias A Lipitakis and published by World Scientific Publishing Company. This book was released on 1993-11-19 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains selected papers of the proceedings of the first Hellenic Conference on Mathematics and Informatics (HERMIS '92). The main theme for HERMIS '92 Conference was Computer Mathematics, with special emphasis on Computational Mathematics, Operational Research and Statistics, and Mathematics in Economic Science. The presented papers of the HERMIS Conference have been classified into the following technical sessions: Numerical solution of Differential Equations, Parallel Processing and Parallel Algorithms, Optimization and Approximation, Algorithms in Operational Research and Control Theory, Statistical Methods and Analysis, Mathematics in Economic Science, Artificial Intelligence and Data Bases Technology.In addition, a number of selected research articles published recently in the Hellenic Mathematical Society Bulletin in the form of special issues on Computer Mathematics (Volumes 31 and 32) are also included.
Download or read book A Multilevel Parallel Solver for Block Tridiagonal and Banded Linear Systems written by Ibrahim N. Hajj and published by . This book was released on 1989 with total page 31 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper describes an efficient algorithm for the parallel solution of systems of linear equations with a block tridiagonal coefficient matrix. The algorithm comprises a multilevel LU-factorization based on block cyclic reduction and a corresponding solution algorithm. The paper includes a general presentation of the parallel multilevel LU-factorization and solution algorithms, but the main emphasis is on implementation principles for a message passing computer with hypercube topology. Problem partitioning, processor allocation and communication requirements are discussed for the general block tridiagonal algorithm. Keywords: Parallel solver, banded linear systems, block tridiagonal, cyclic reduction, multilevel decomposition, hypercube, multiprocessing. (KR).
Download or read book Accelerated Iterative Methods for the Solution of Tridiagonal Systems on Parallel Computers written by D. E. Heller and published by . This book was released on 1974 with total page 33 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors consider iterative methods for the solution of tridiagonal systems and present a new iteration whose rate of convergence is comparable to that of the optimal two-cyclic Chebyshev iteration but which does not require the calculation of optimal parameters. The theory has a natural extension to block tridiagonal systems. Numerical experiments suggest that on a parallel computer this new algorithm is the best of the iterative algorithms considered.
Download or read book Energy Research Abstracts written by and published by . This book was released on 1990 with total page 852 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Numerical Computations with GPUs written by Volodymyr Kindratenko and published by Springer. This book was released on 2014-07-03 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book brings together research on numerical methods adapted for Graphics Processing Units (GPUs). It explains recent efforts to adapt classic numerical methods, including solution of linear equations and FFT, for massively parallel GPU architectures. This volume consolidates recent research and adaptations, covering widely used methods that are at the core of many scientific and engineering computations. Each chapter is written by authors working on a specific group of methods; these leading experts provide mathematical background, parallel algorithms and implementation details leading to reusable, adaptable and scalable code fragments. This book also serves as a GPU implementation manual for many numerical algorithms, sharing tips on GPUs that can increase application efficiency. The valuable insights into parallelization strategies for GPUs are supplemented by ready-to-use code fragments. Numerical Computations with GPUs targets professionals and researchers working in high performance computing and GPU programming. Advanced-level students focused on computer science and mathematics will also find this book useful as secondary text book or reference.
Download or read book Accuracy and Stability of Numerical Algorithms written by Nicholas J. Higham and published by SIAM. This book was released on 2002-01-01 with total page 710 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Numerical Methods for General and Structured Eigenvalue Problems written by Daniel Kressner and published by Springer Science & Business Media. This book was released on 2006-01-20 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is about computing eigenvalues, eigenvectors, and invariant subspaces of matrices. Treatment includes generalized and structured eigenvalue problems and all vital aspects of eigenvalue computations. A unique feature is the detailed treatment of structured eigenvalue problems, providing insight on accuracy and efficiency gains to be expected from algorithms that take the structure of a matrix into account.
Download or read book Government Reports Index written by and published by . This book was released on 1973 with total page 1124 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Reviews in Numerical Analysis 1980 86 written by and published by . This book was released on 1987 with total page 744 pages. Available in PDF, EPUB and Kindle. Book excerpt: These five volumes bring together a wealth of bibliographic information in the area of numerical analysis. Containing over 17,600 reviews of articles, books, and conference proceedings, these volumes represent all the numerical analysis entries that appeared in Mathematical Reviews between 1980 and 1986. Author and key indexes appear at the end of volume 5.
