Handbook of Numerical Analysis: Solution of Equations in Rn (Prt 4), Techniques of Scientific Computer (Part 4), Numerical Methods for Fluids, Part 2

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Philippe G. Ciarlet, Jacques Louis Lions
Gulf Professional Publishing, Dec 1, 2001 - Mathematics - 661 pages
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This series of volumes covers all the major aspects of numerical analysis, serving as the basic reference work on the subject. Each volume concentrates on one to three particular topics. Each article, written by an expert, is an in-depth survey, reflecting up-to-date trends in the field, and is essentially self-contained. The handbook will cover the basic methods of numerical analysis, under the following general headings: solution of equations in Rn; finite difference methods; finite element methods; techniques of scientific computing; optimization theory; and systems science. It will also cover the numerical solution of actual problems of contemporary interest in applied mathematics, under the following headings: numerical methods for fluids; numerical methods for solids; and specific applications - including meteorology, seismology, petroleum mechanics and celestial mechanics.

 

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Contents

Introduction
9
Basic Theory
21
Jacobis Method
31
Methods for the Complete Eigenproblem
37
Krylov Subspaces
53
The Lanczos Method
61
Lanczos in finite precision
74
Alternative approximations
75
The JacobiDavidson iteration method
122
The iterative solution of the correction equation
125
A numerical example
127
A simple JacobiDavidson algorithm
128
Restart and deflation strategies
130
Preconditioning
133
A complete algorithm
134
Harmonic Ritz values
137

Accuracy of harmonic Ritz values g I
81
Refined eigenvector approximations
82
Amoldis Method
85
Numerical examples X6 30 Shiftandinvert m
86
Implicitly Restarted Amoldi
92
Harmonic Ritz values for Araoldis process
96
Numerical examples
98
The TwoSided Lanczos Method
101
Numerical example
106
Harmonic Petrov values for BiLanczos
108
Breakdown and Lookahead 11
112
JacobiDavidson Methods
115
Numerical example I jg 40 Davidsons method and preconditioning
119
The methods of Jacobi
120
Generalized Eigenproblems
139
Reduction to standard form
140
Rational Krylov methods
142
The JacobiDavidson QZ method
145
An example of a generalized eigenproblem
149
Polynomial and Constrained Eigenproblems
153
Quadratic eigenvalue problems
154
Higher order polynomial eigenvalue problems
157
Constrained eigenproblems
160
Related Issues
163
REFERENCES
169
SUBJECT INDEX
177
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