"This book is concerned with solving very large sets of linear equations, where each equation involves only a small number of variables. Many applications involve equations of this kind and they often need to be solved repeatedly as their entries change.Very special methods are needed to make these calculations feasible. The authors have been involved in designing special algorithms and writing codes to implement them for over 40 years. This book aims to describe in a clear and simple way those algorithms that have stood the test of time, as well as those that have been developed recently to enable the efficient solution of far larger systems and to take advantage hardware"--

Direct Methods for Sparse Matrices (Numerical Mathematics and Scientific Computation)

Science & Math

Duff, Iain S.

Mathematics

Oxford University Press

This book provides practical approaches to the efficient use of sparsity--a key to solving large problems in many fields, including computational science and engineering, where mathematical models give rise to very large systems of linear equations. The emphasis is on practicality, with conclusions based on concrete experience. Non-numeric computing techniques have been included as well as frequent illustrations in an attempt to bridge the gap between the written word and the working computer code. Exercises have been included to strengthen understanding of the material as well as to extend it for students and researchers in engineering, mathematics, and computer science.

Direct Methods for Sparse Matrices (Monographs on Numerical Analysis)

Erisman, A. M.

Reid, John Ker

This book presents a unified treatment of recently developed techniques and current understanding about solving systems of linear equations and large scale eigenvalue problems on high-performance computers. It provides a rapid introduction to the world of vector and parallel processing for these linear algebra applications. Topics include major elements of advanced-architecture computers and their performance, recent algorithmic development, and software for direct solution of dense matrix problems, direct solution of sparse systems of equations, iterative solution of sparse systems of equations, and solution of large sparse eigenvalue problems. This book supercedes the SIAM publication Solving Linear Systems on Vector and Shared Memory Computers, which appeared in 1990. The new book includes a considerable amount of new material in addition to incorporating a substantial revision of existing text.

Numerical Linear Algebra on High-Performance Computers (Software, Environments and Tools, Series Number 7)

Computers & Technology

Dongarra, Jack J.

Sorensen, Danny C.

van der Vorst, Hank A.

Programming

Society for Industrial and Applied Mathematics

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