Numerical Linear Algebra, Digital Signal Processing and Parallel Algorithms

1. Front Matter

   Pages I-XIII

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2. Invited Lectures

   1. The Family of Fast Least Squares Algorithms for Adaptive Filtering

      • M. G. Bellanger

      Pages 1-18

   2. Adaptive Control Algorithms

      • Robert R. Bitmead

      Pages 19-40

   3. Error Analysis of Least Squares Algorithms

      • Åke Björck

      Pages 41-73

   4. Parallel Algorithms for Toeplitz Systems

      • Richard P. Brent

      Pages 75-92

   5. Parallel Algorithms for Digital Signal Processing

      • Richard P. Brent

      Pages 93-110

   6. An Introduction to the Class of Split Levinson Algorithms

      • P. Delsarte, Y. Genin

      Pages 111-130

   7. On the Split Approach Based Algorithms for DSP Problems

      • P. Delsarte, Y. Genin

      Pages 131-147

   8. Updating and Downdating of Orthogonal Polynomials with Data Fitting Applications

      • Sylvan Elhay, Gene H. Golub, Jaroslav Kautsky

      Pages 149-172

   9. Parallel Algorithms for Singular Value Problems

      • Sven Hammarling

      Pages 173-187

   10. Some Remarks on the Generalised Bareiss and Levinson Algorithms

       • Ilse Ipsen

       Pages 189-214

   11. Generalized Displacement Structure for Block-Toeplitz, Toeplitz-block, and Toeplitz-derived Matrices

       • J. Chun, T. Kailath

       Pages 215-236

   12. Fault Tolerant Recursive Least Squares Minimization

       • Franklin T. Luk

       Pages 237-250

   13. A Systolic Array for Recursive Least Squares Minimisation and Adaptive Beamforming

       • J. G. McWhirter

       Pages 251-287

   14. Parallel Algorithms for Supercomputers

       • Gérard Meurant

       Pages 289-318

   15. Updating Techniques in Parallel Computation

       • D. C. Sorensen

       Pages 319-319

   16. On the Use of the Singular Value Decomposition in Identification and Signal Processing

       • Joos Vandewalle, Bart De Moor

       Pages 321-360

   17. Structured Linear Algebra Problems in Digital Signal Processing

       • Paul M. Van Dooren

       Pages 361-384

3. Contributed Lectures

   1. Constructing a Unitary Hessenberg Matrix from Spectral Data

      • Gregory Ammar, William Gragg, Lothar Reichel

      Pages 385-395

   2. Parallel Computation of the Generalized Singular Value Decomposition

      • Zhaojun Bai

      Pages 397-399

Numerical linear algebra, digital signal processing, and parallel algorithms are three disciplines with a great deal of activity in the last few years. The interaction between them has been growing to a level that merits an Advanced Study Institute dedicated to the three areas together. This volume gives an account of the main results in this interdisciplinary field. The following topics emerged as major themes of the meeting: - Singular value and eigenvalue decompositions, including applications, - Toeplitz matrices, including special algorithms and architectures, - Recursive least squares in linear algebra, digital signal processing and control, - Updating and downdating techniques in linear algebra and signal processing, - Stability and sensitivity analysis of special recursive least squares problems, - Special architectures for linear algebra and signal processing. This book contains tutorials on these topics given by leading scientists in each of the three areas. A consider- able number of new research results are presented in contributed papers. The tutorials and papers will be of value to anyone interested in the three disciplines.

• Algorithmus
• Eigenvalue
• Eigenwertproblem
• algebra
• algorithm
• algorithms
• digital signal processing
• eigenvalue problem
• eigenvalue problems
• linear algebra
• numerical mathematics
• numerische Mathematik
• parallel computing
• signal processing
• stability
• algorithm analysis and problem complexity

• Computer Science Department, Stanford University, Stanford, USA

  Gene H. Golub

• Philips Research Laboratory, Louvain-la-Neuve, Belgium

  Paul Dooren

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