This book presents the description of the state of modern iterative techniques together with systematic analysis. The first chapters discuss the classical methods. Comprehensive chapters are devoted to semi-iterative techniques (Chebyshev methods), transformations, incomplete decompositions, gradient and conjugate gradient methods, multi-grid methods and domain decomposition techniques (including e.g. the additive and multiplicative Schwartz method). In contrast to other books all techniques are described algebraically. For instance, for the domain decomposition method this is a new but helpful approach. Every technique described is illustrated by a Pascal program applicable to a class of model problem.
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Text: English (translation)
Original Language: German
Original Language: German
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Inside This Book
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First Sentence:
Iterative methods are almost 170 years old. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
symmetric iteration, asymptotical convergence rate, secondary iteration, composed iteration, starting iterate, corresponding matrix norm, inner grid points, basic iteration, smoothing iteration, numerical radius, iteration matrix, regular splitting, conjugate residuals, iteration matrices, product iteration, third normal form, ordered index set, consistent iteration, nested iteration, smoothing property, extreme eigenvalues, spectral norm, contraction number, energy norm, domain decomposition methods Key Phrases - Capitalized Phrases (CAPs): (learn more)
Block Versions, Generation of Iterations, German Chamber of Commerce, Numerical Examples Table, Properties of the Additive Schwarz Iteration, Supplementary Remarks, The Method of the Conjugate Directions New!
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Iterative methods are almost 170 years old. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
symmetric iteration, asymptotical convergence rate, secondary iteration, composed iteration, starting iterate, corresponding matrix norm, inner grid points, basic iteration, smoothing iteration, numerical radius, iteration matrix, regular splitting, conjugate residuals, iteration matrices, product iteration, third normal form, ordered index set, consistent iteration, nested iteration, smoothing property, extreme eigenvalues, spectral norm, contraction number, energy norm, domain decomposition methods Key Phrases - Capitalized Phrases (CAPs): (learn more)
Block Versions, Generation of Iterations, German Chamber of Commerce, Numerical Examples Table, Properties of the Additive Schwarz Iteration, Supplementary Remarks, The Method of the Conjugate Directions New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
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This book cites 75
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80
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- Linear Operator Theory in Engineering and Science (Applied Mathematical Sciences) by Arch W. Naylor in Front Matter
- Sturmian Theory for Ordinary Differential Equations (Applied Mathematical Sciences) by William T. Reid in Front Matter
- Lectures on Viscoelasticity Theory (Applied Mathematical Sciences) by A.C. Pipkin in Front Matter
- Averaging Methods in Nonlinear Dynamical Systems (Applied Mathematical Sciences) by Jan A. Sanders in Back Matter
- Differential Equations by K. A. Stroud in Front Matter
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- Multiscale Wavelet Methods for Partial Differential Equations, Volume 6 (Wavelet Analysis and Its Applications) by Wolfgang Dahmen on page 55, page 378, and page 435
- Conjugate Gradient Algorithms and Finite Element Methods (Scientific Computation) by Michal Krizek on page 209, and Back Matter
- Recent Progress in Computational and Applied PDEs: Conference Procedings for the International Conference Held in Zhangjiajie in July 2001 by Tony Chan on page 380, and page 419
- Advanced Topics in Computational Partial Differential Equations: Numerical Methods and Diffpack Programming (Lecture Notes in Computational Science and Engineering) by Hans Petter Langtangen on page 150, and page 236
- Scientific Computing in Electrical Engineering: Proceedings of SCEE2002 (Mathematics in Industry / The European Consortium for Mathematics in Industry) (v. 4) by Wilhelmus H. Schilders on page 288
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