Since the first edition of this book was published in 1996, tremendous progress has been made in the scientific and engineering disciplines regarding the use of iterative methods for linear systems. The size and complexity of the new generation of linear and nonlinear systems arising in typical applications has grown. Solving the 3-dimensional models of these problems using direct solvers is no longer effective. At the same time, parallel computing has penetrated these application areas, become less expensive and standardized. Iterative methods are easier than direct solvers to implement on parallel computers, but require different approaches and solution algorithms than classical methods. Iterative Methods for Sparse Linear Systems gives an in-depth, up-to-date view of practical algorithms for solving large-scale linear systems of equations. These equations can number in the millions and are sparse in the sense that they each involve only a small number of unknowns. The methods described are iterative, i.e., they provide sequences of approximations that will converge to the solution. This new edition includes a wide range of the best methods available today. The author has added a new chapter on multigrid techniques and has updated material throughout the text, particularly the chapters on sparse matrices, Krylov subspace methods, preconditioning techniques, and parallel preconditioners. Material on older topics has been removed or shortened, numerous exercises have been added, and many typographical errors have been corrected. The updated and expanded bibliography now includes more recent works emphasizing new and important topics in this field.
Yousef Saad joined the University of Minnesota in 1990 as a Professor of Computer Science and a Fellow of the Minnesota Supercomputer Institute. He was head of the Department of Computer Science and Engineering from 1997 to 2000. He received the Doctorat d'Etat from the University of Grenoble (France) in 1983. His current research interests include numerical linear algebra, sparse matrix computations, iterative methods, parallel computing, and numerical methods for eigenvalue problems.
Preface to the Second Edition Preface to the First Edition Chapter 1: Background in Linear Algebra Chapter 2: Discretization of Partial Differential Equations Chapter 3: Sparse Matrices Chapter 4: Basic Iterative Methods Chapter 5: Projection Methods Chapter 6: Krylov Subspace Methods, Part I Chapter 7: Krylov Subspace Methods, Part II Chapter 8: Methods Related to the Normal Equations Chapter 9: Preconditioned Iterations Chapter 10: Preconditioning Techniques Chapter 11: Parallel Implementations Chapter 12: Parallel Preconditioners Chapter 13: Multigrid Methods Chapter 14: Domain Decomposition Methods Bibliography Index
