Perturbation Theory for Matrix Equations

C.K. Chui, P. Monk and L. Wuytack (Eds.)9780080538679, 9780444513151, 0444513159

The book is devoted to the perturbation analysis of matrix equations. The importance of perturbation analysis is that it gives a way to estimate the influence of measurement and/or parametric errors in mathematical models together with the rounding errors done in the computational process. The perturbation bounds may further be incorporated in accuracy estimates for the solution computed in finite arithmetic. This is necessary for the development of reliable computational methods, algorithms and software from the viewpoint of modern numerical analysis.
In this book a general perturbation theory for matrix algebraic equations is presented. Local and non-local perturbation bounds are derived for general types of matrix equations as well as for the most important equations arising in linear algebra and control theory. A large number of examples, tables and figures is included in order to illustrate the perturbation techniques and bounds.
Key features:
• The first book in this field • Can be used by a variety of specialists • Material is self-contained • Results can be used in the development of reliable computational algorithms • A large number of examples and graphical illustrations are given • Written by prominent specialists in the field

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Table of contents :
Content:
Preface
Pages v-vi

Chapter 1 Introduction
Pages 1-7

Chapter 2 Perturbation problems Original Research Article
Pages 9-28

Chapter 3 Problems with explicit solutions Original Research Article
Pages 29-50

Chapter 4 Problems with implicit solutions Original Research Article
Pages 51-75

Chapter 5 Lyapunov majorants Original Research Article
Pages 77-101

Chapter 6 Singular problems Original Research Article
Pages 103-111

Chapter 7 Perturbation bounds Original Research Article
Pages 113-120

Chapter 8 General sylvester equations Original Research Article
Pages 121-154

Chapter 9 Specific Sylvester equations Original Research Article
Pages 155-173

Chapter 10 General Lyapunov equations Original Research Article
Pages 175-200

Chapter 11 Lyapunov equations in control theory Original Research Article
Pages 201-221

Chapter 12 General quadratic equations Original Research Article
Pages 223-238

Chapter 13 Continuous-time Riccati equations Original Research Article
Pages 239-266

Chapter 14 Coupled Riccati equations Original Research Article
Pages 267-285

Chapter 15 General fractional-affine equations Original Research Article
Pages 287-302

Chapter 16 Symmetric fractional-affine equations Original Research Article
Pages 303-326

Appendix A Elements of algebra and analysis
Pages 327-343

Appendix B Unitary and orthogonal decompositions
Pages 345-355

Appendix C Kronecker product of matrices
Pages 357-361

Appendix D Fixed point principles
Pages 363-369

Appendix E Sylvester operators
Pages 371-377

Appendix F Lyapunov operators
Pages 379-395

Appendix G Lyapunov-like operators
Pages 397-400

Appendix H Notation
Pages 401-406

Bibliography
Pages 407-424

Index
Pages 425-429