Matrix Preconditioning Techniques and Applications

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Cambridge University Press, Jul 14, 2005 - Mathematics - 568 pages
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Preconditioning techniques have emerged as an essential part of successful and efficient iterative solutions of matrices. Ke Chen's book offers a comprehensive introduction to these methods. A vast range of explicit and implicit sparse preconditioners are covered, including the conjugate gradient, multi-level and fast multi-pole methods, matrix and operator splitting, fast Fourier and wavelet transforms, incomplete LU and domain decomposition, Schur complements and approximate inverses. In addition, aspects of parallel realization using the MPI are discussed. Very much a users-guide, the book provides insight to the use of these techniques in areas such as acoustic wave scattering, image restoration and bifurcation problems in electrical power stations. Supporting MATLAB files are available from the Web to support and develop readers' understanding, and provide stimulus for further study. Pitched at graduate level, the book is intended to serve as a useful guide and reference for students, computational practitioners, engineers and researchers alike.
  

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Contents

Direct methods
66
Iterative methods
110
direct approximation
165
direct
191
coarse grid
240
Multilevel recursive Schur complements
289
approximation
310
Wavelet Schur preconditioners T6
340
coupled matrix problems
400
image restoration and inverse problems
416
voltage stability in electrical power systems
449
Parallel computing by examples
475
a brief guide to linear algebra
504
The Jordan decomposition
507
list of supplied Mfiles and programs
523
Author Index
556

Implicit wavelet preconditioners T7
364
acoustic scattering modelling
383

Common terms and phrases

Popular passages

Page 539 - New methods for computing a closest saddle node bifurcation and worst case load power margin for voltage collapse", IEEE Trans, on Power Systems, vol.
Page 546 - YEREMIN, On a family of two-level preconditionings of the incomplete block factorization type, Soviet J.
Page 531 - A survey of preconditioned iterative methods for linear systems of algebraic equations".
Page 540 - Duff and J. Koster. On algorithms for permuting large entries to the diagonal of a sparse matrix.
Page 535 - VH Quintana. Comparison of Performance Indices for Detection of Proximity to Voltage Collapse.
Page 537 - On a class of preconditioning methods for dense linear systems from boundary elements, SIAM J. Sci.

References to this book

About the author (2005)

Dr Chen is a Reader in Applied Mathematics at the University of Liverpool.

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