Large linear systems of equations arise in most scientific problems where mathematical models are used. The most efficient methods for solving these equations are iterative methods. The first part of this book contains basic and classical material from the study of linear algebra and numerical linear algebra. The second half of the book is unique among books on this topic, because it is devoted to the construction of preconditioners and iterative acceleration methods of the conjugate gradient type. This book is for graduate students and researchers in numerical analysis and applied mathematics.
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Editorial Reviews
Review
"...the book is the most complete and interesting study of iterative methods for systems of linear equations to date. I strongly recommend it to any researcher in the field or in any other area in which the solution of large systems of linear equations plays an important role...it will become a standard reference in numerical linear algebra..." Joaquim J. Judice, Mathematical Reviews
"The author has done a fine job of collecting the plethora of work in this area into an up-to-date, coherent entity....I am sure that this volume is destined to be the bible of iterative methods for many years to come." T. Hopkins, Computing Reviews
"...contains a wealth of relevant mathematical theory which underpins much of the development of this specific but important area of Numerical Linear Algebra. It is likely to be an important reference for theoreticians interested in the development and analysis of iterative solution methods for years to come." A. Wathen, The Bulletin of the Institute of Mathematics and its Applications
"The author has done a fine job of collecting the plethora of work in this area into an up-to-date, coherent entity....I am sure that this volume is destined to be the bible of iterative methods for many years to come." T. Hopkins, Computing Reviews
"...contains a wealth of relevant mathematical theory which underpins much of the development of this specific but important area of Numerical Linear Algebra. It is likely to be an important reference for theoreticians interested in the development and analysis of iterative solution methods for years to come." A. Wathen, The Bulletin of the Institute of Mathematics and its Applications
Book Description
The first part of this text contains basic and classical material from the study of linear algebra and numerical linear algebra. The second half is unique among texts on this topic, because it is devoted to the construction of preconditioners and iterative acceleration methods of the conjugate gradient type.
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1 of 1 people found the following review helpful:
4.0 out of 5 stars
fast convergence for some problems,
By
This review is from: Iterative Solution Methods (Paperback)
The book may be attractive to researchers dealing with large linear systems of equations, and hoping to solve these in some quick fashion. Axelsson discusses iterative methods that he claims can converge rapidly. While this may not be generally true, the pragmatic researcher might keep Axelsson's ideas in mind, and consider applying them to her problems.
The first section of the book is somewhat mundane. Totally standard descriptions that can be found in many texts on linear algebra. But the value of the book is in the second section. Where the author offers neat suggestions on how to pick the initial conditions for starting the iterations. As well as a type of steepest gradient descent to speed up the convergence.
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Inside This Book
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First Sentence:
The need to solve large linear systems of algebraic equations arises in almost any mathematical model, as illustrated in the instances below. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
incomplete factorization method, inverse free form, average convergence factor, convergent splittings, offdiagonal entries, weak regular splitting, diagonal compensation, block matrix entries, generalized conjugate gradient method, preconditioning methods, elliptic difference equations, complement matrices, basic iterative methods, numerical radius, reordering method, eigenvector space, block tridiagonal form, annihilating polynomial, pivot entries, superlinear rate, preconditioning matrix, extreme eigenvalues, spectral condition number, preconditioned matrix, sparsity pattern Key Phrases - Capitalized Phrases (CAPs): (learn more)
New York, Proof Let, Englewood Cliffs, Matrix Anal, Proof Note, Prentice Hall, Technical Report, Chalmers University of Technology, Numer Anal, Proof Lemma, Research Report, Department of Computer Sciences, Mathematical Sciences, The Netherlands, Data Handling Division, Its Applic, Numer Math, Proof Theorem, The Theory of Matrices New!
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
The need to solve large linear systems of algebraic equations arises in almost any mathematical model, as illustrated in the instances below. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
incomplete factorization method, inverse free form, average convergence factor, convergent splittings, offdiagonal entries, weak regular splitting, diagonal compensation, block matrix entries, generalized conjugate gradient method, preconditioning methods, elliptic difference equations, complement matrices, basic iterative methods, numerical radius, reordering method, eigenvector space, block tridiagonal form, annihilating polynomial, pivot entries, superlinear rate, preconditioning matrix, extreme eigenvalues, spectral condition number, preconditioned matrix, sparsity pattern Key Phrases - Capitalized Phrases (CAPs): (learn more)
New York, Proof Let, Englewood Cliffs, Matrix Anal, Proof Note, Prentice Hall, Technical Report, Chalmers University of Technology, Numer Anal, Proof Lemma, Research Report, Department of Computer Sciences, Mathematical Sciences, The Netherlands, Data Handling Division, Its Applic, Numer Math, Proof Theorem, The Theory of Matrices 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)
This book cites 29
books:
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81
books
cite this book:
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- Matrix Computations (Johns Hopkins Studies in Mathematical Sciences)(3rd Edition) by Gene H. Golub on 4 pages
- Nonnegative Matrices in the Mathematical Sciences (Classics in Applied Mathematics) by Abraham Berman on page 121, page 249, and page 311
- Computational Methods of Linear Algebra by V. N. Faddeeva on page 82, and Back Matter
- Matrix Iterative Analysis (Springer Series in Computational Mathematics) by Richard S. Varga on page 157, and page 312
- Matrix Analysis by Roger A. Horn on page 121, and page 157
See all 29 books this book cites
- Fast Solution of Discretized Optimization Problems (International Series of Numerical Mathematics) by Karl-Heinz Hoffmann on page 16, and page 33
- Large-Scale Scientific Computing: 5th International Conference, LSSC 2005, Sozopol, Bulgaria, June 6-10, 2005, Revised Papers (Lecture Notes in ... Computer Science and General Issues) by Ivan Lirkov on page 13, and page 685
- Numerical Analysis and Its Applications: Second International Conference, NAA 2000 Rousse, Bulgaria, June 11-15, 2000. Revised Papers (Lecture Notes in Computer Science) by Lubin Vulkov on page 480, and page 489
- Numerical Challenges in Lattice Quantum Chromodynamics: Joint Interdisciplinary Workshop of John von Neumann Institute for Computing, Jülich and ... in Computational Science and Engineering) by Andreas Frommer on page 27, and page 96
- Numerical Computation in Science and Engineering by C. Pozrikidis on page 178
See all 81 books citing this book
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