Much recent research has concentrated on the efficient solution of large sparse or structured linear systems using iterative methods. A language loaded with acronyms for a thousand different algorithms has developed, and it is often difficult even for specialists to identify the basic principles involved. Here is a book that focuses on the analysis of iterative methods. The author includes the most useful algorithms from a practical point of view and discusses the mathematical principles behind their derivation and analysis. Several questions are emphasized throughout: Does the method converge? If so, how fast? Is it optimal, among a certain class? If not, can it be shown to be near-optimal? The answers are presented clearly, when they are known, and remaining important open questions are laid out for further study.
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Editorial Reviews
Review
'This graduate-level textbook gives equal weights to iterative methods and preconditioning (including domain decomposition and multigrid), and it approaches Krylov space methods from a somewhat different angle. It also treats some subjects that appear for the first time in a textbook, like new results on roundoff effects in the Lanczos and conjugate gradient algorithms. This well-done introduction to the area can be strongly recommended. It is competently written by an author who has contributed much to the complete reshaping of this field in the last twenty years.' Martin H. Gutknecht, ETH Zurich
'For a course in matrix iterations, this is just the right book. It is wide-ranging, careful about details, and appealingly written - a major addition to the literature in this important area.' Nick Trefethen, Professor of Numerical Analysis, Oxford University
'This book differs substantially from other books on iterative methods, including those recently published, in that it concentrates on several principles behind the derivation and analysis of the most important methods and preconditioning techniques. Individual algorithms serve as examples illustrating the discussed ideas. Strong emphasis is given to motivation and its relation to problems in other areas of mathematics. The book speaks in clear language about principal problems in the area of iterative methods. It represents a comprehensive introduction to the field and stimulates the interest of the reader. It is valuable for students and also for experts working in the area of iterative methods.' Zdenek Strakos, Professor, Czech Academy of Sciences, Institute of Computer Science.
'Anne Greenbaum is an admired authority in the field of iterative methods. Engineers and scientists often ask me about the puzzling behavior of iterative methods, which I almost always answer with a reference to Anne's work, now made easy to point to in her new book.' Paul Saylor, Department of Computer Science, University of Illinois, Urbana-Champaign
'For a course in matrix iterations, this is just the right book. It is wide-ranging, careful about details, and appealingly written - a major addition to the literature in this important area.' Nick Trefethen, Professor of Numerical Analysis, Oxford University
'This book differs substantially from other books on iterative methods, including those recently published, in that it concentrates on several principles behind the derivation and analysis of the most important methods and preconditioning techniques. Individual algorithms serve as examples illustrating the discussed ideas. Strong emphasis is given to motivation and its relation to problems in other areas of mathematics. The book speaks in clear language about principal problems in the area of iterative methods. It represents a comprehensive introduction to the field and stimulates the interest of the reader. It is valuable for students and also for experts working in the area of iterative methods.' Zdenek Strakos, Professor, Czech Academy of Sciences, Institute of Computer Science.
'Anne Greenbaum is an admired authority in the field of iterative methods. Engineers and scientists often ask me about the puzzling behavior of iterative methods, which I almost always answer with a reference to Anne's work, now made easy to point to in her new book.' Paul Saylor, Department of Computer Science, University of Illinois, Urbana-Champaign
Book Description
Here is a book that focuses on the analysis of iterative methods for solving linear systems. The author includes the most useful algorithms from a practical point of view and discusses the mathematical principles behind their derivation and analysis.
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5.0 out of 5 stars
A good introduction to iterative methods.,
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This review is from: Iterative Methods for Solving Linear Systems (Frontiers in Applied Mathematics) (Paperback)
This book as well at the one from Kelley is a great introduction to iterative methods for solving linear systems. I particularly like the chapters on Preconditioners.
5.0 out of 5 stars
SIAM is SIAM!!,
This review is from: Iterative Methods for Solving Linear Systems (Frontiers in Applied Mathematics) (Paperback)
Totally awesome and well organized contents are in this material. Nice book to get the knowledge of numerical linear algebra!!!
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Inside This Book
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First Sentence:
The subject of this book is what at first appears to be a very simple problem-how to solve the system of linear equations Ax = b, where A is an n-by-n nonsingular matrix and b is a given n-vector. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
kth rotation, preconditioned matrix, positive definite problems, minimax polynomial, residual norm, simple iteration method, finite precision computation, regular splitting, zero initial guess, indefinite problems, numerical radius, original linear system, short recurrence, relaxation sweep, finite precision arithmetic, diagonal preconditioner, recurrence coefficients, nonsymmetric linear systems, large overestimate, asymptotic convergence rate, linear system solvers, sparsity pattern, multigrid methods, residual algorithm, tiny intervals Key Phrases - Capitalized Phrases (CAPs): (learn more)
Hermitian Lanczos, Near-Optimal Approximation New!
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
The subject of this book is what at first appears to be a very simple problem-how to solve the system of linear equations Ax = b, where A is an n-by-n nonsingular matrix and b is a given n-vector. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
kth rotation, preconditioned matrix, positive definite problems, minimax polynomial, residual norm, simple iteration method, finite precision computation, regular splitting, zero initial guess, indefinite problems, numerical radius, original linear system, short recurrence, relaxation sweep, finite precision arithmetic, diagonal preconditioner, recurrence coefficients, nonsymmetric linear systems, large overestimate, asymptotic convergence rate, linear system solvers, sparsity pattern, multigrid methods, residual algorithm, tiny intervals Key Phrases - Capitalized Phrases (CAPs): (learn more)
Hermitian Lanczos, Near-Optimal Approximation New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
49
books
cite this book:
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- Linear Algebra - Linear Systems and Eigenvalues, Volume 3 by P.M. van Dooren on page 29, page 196, and page 291
- The Finite Element Method in Electromagnetics by Jian-Ming Jin on page 486, and page 635
- Fundamentals of Matrix Computations by David S. Watkins in Back Matter
- Introduction to Parallel Computing (Oxford Texts in Applied and Engineering Mathematics) by W. P. Petersen in Back Matter
- Smart Material Systems: Model Development (Frontiers in Applied Mathematics) by Ralph Smith in Front Matter
See all 49 books citing this book
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