Fast Reliable Algorithms for Matrices with Structure

This book is the first to pay special attention to the combined issues of speed and numerical reliability in algorithm development. These two requirements have often been regarded as competitive, so much so that the design of fast and numerically reliable algorithms for large-scale structured systems of linear equations, in many cases, remains a significant open issue. Fast Reliable Algorithms for Matrices with Structure helps bridge this gap by providing the reader with recent contributions written by leading experts in the field. The authors deal with both the theory and the practice of fast numerical algorithms for large-scale structured linear systems. Each chapter covers in detail different aspects of the most recent trends in the theory of fast algorithms, with emphasis on implementation and application issues. Both direct and iterative methods are covered.

Spis treści:
Contributors
Preface
Notation
1. Displacement structure and array algorithms Thomas Kailath
2. Stabilized Schur Algorithms Shivkumar Chandrasekaran and Ali H. Sayed
3. Fast Stable Solvers for Structured Linear Systems Ali H. Sayed and Shivkumar Chandrasekaran
4. Stability of Fast Algorithms for Structured Linear Systems Richard P. Brent
5. Iterative Methods for Linear Systems with Matrix Structure Raymond H. Chan and Michael K. Ng
6. Asymptotic Spectral Distribution of Toeplitz-Related Matrices Paolo Tilli
7. Newtons Iteration for Structured Matrices Victor Y. Pan, Sheryl Branham, Rhys E. Rosholt and Ai-Long Zheng
8. Fast Algorithms with Applications to Markov Chains and Queueing Models Dario A. Bini and Beatrice Meini
9. Tensor Displacement Structures and Polyspectral Matching Victor S. Grigorascu and Phillip A. Regalia
10. Minimal Complexity Realization of Structured Matrices Patrick Dewilde
Appendix A. Useful Matrix Results Thomas Kailath and Ali H. Sayed
Appendix B. Elementary Transformations Thomas Kailath and Ali H. Sayed
Bibliography
Index.