Accurate Numerical Algorithms: A Collection of Research Papers

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Christian Ullrich, Jürgen Wolff) von Gudenberg
Springer-Verlag, 1989 - Computers - 234 pages
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Contents

Introduction
ix
Design of EMethods 3
ix
Application of Brouwers FixedPoint Theorem 4
ix
Eigenvalues
9
The Application of Theorems on Zeros in the Complex Plane
10
Linear Systems for Sparse Matrices
12
Quadrature
13
Nonlinear Systems
15
Ada Package Specification
109
Test Results
111
Conclusions
114
Frangen V
116
Introduction
117
Refinement of the SchurCohn Algorithm
122
Refined Bisecting Process
126
Solving Algorithm
132

References
16
Lohner
17
Appendix The PASCALSC Demonstration Package
18
Griiner K Solving the Complex Algebraic Eigenvalue Problem with Verified High Accuracy
59
Mathematical Foundations
61
Inclusion of the Complex Algebraic Eigenvalue Problem
63
The Inclusion Algorithm
71
References
78
Moynihan V
79
Implementation
83
Appendix
85
Glossary
86
Enclosing all Eigenvalues of Symmetric Matrices
87
Simple Method for Computing Enclosures of Eigenvalues
89
Computing Eigenvector Approximations with High Accuracy
91
Computing Eigenvalue Enclosures with High Accuracy
94
Computing Eigenvector Enclosures
96
Numerical Examples
97
References
102
Computing Accurate Eigenvalues of a Hermitian Matrix
104
A Jacobi Method for the Hermitian Eigenvalue Problem
105
Inclusion of the Estimated Eigenvalues
107
Adapting the Algorithm to Ada
108
Performance Example
134
Conclusions
135
Verified Results for Linear Systems with Sparse Matrices
137
Method Description
139
Method Implementation
142
Remarks
160
Kelch R SelfValidating Numerical Quadrature
162
Review
163
Fundamentals
164
Verified Computation of the Procedure Error via Automatic Differentiation
168
Numerical Quadrature via Modified RombergExtrapolation
176
Faster Reduction of the Total Error via Adaptive Refinement
185
Numerical Results
199
References
202
Schumacher G Solving Nonlinear Equations with Verification of Results
203
Inclusion of Zeros
205
Numerical Problems with Traditional Methods
216
Improvement of Theoretical Behaviour of Traditional Methods
223
Condition of a System of Nonlinear Equations
226
Implementation Aspects
227
References
231
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