Numerical Linear Algebra, Digital Signal Processing and Parallel Algorithms

✍ Scribed by M. G. Bellanger (auth.), Gene H. Golub, Paul Van Dooren (eds.)

• Publisher: Springer-Verlag Berlin Heidelberg
• Year: 1991
• Tongue: English
• Leaves: 716
• Series: NATO ASI Series 70
• Edition: 1
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Front Matter....Pages I-XIII
The Family of Fast Least Squares Algorithms for Adaptive Filtering....Pages 1-18
Adaptive Control Algorithms....Pages 19-40
Error Analysis of Least Squares Algorithms....Pages 41-73
Parallel Algorithms for Toeplitz Systems....Pages 75-92
Parallel Algorithms for Digital Signal Processing....Pages 93-110
An Introduction to the Class of Split Levinson Algorithms....Pages 111-130
On the Split Approach Based Algorithms for DSP Problems....Pages 131-147
Updating and Downdating of Orthogonal Polynomials with Data Fitting Applications....Pages 149-172
Parallel Algorithms for Singular Value Problems....Pages 173-187
Some Remarks on the Generalised Bareiss and Levinson Algorithms....Pages 189-214
Generalized Displacement Structure for Block-Toeplitz, Toeplitz-block, and Toeplitz-derived Matrices....Pages 215-236
Fault Tolerant Recursive Least Squares Minimization....Pages 237-250
A Systolic Array for Recursive Least Squares Minimisation and Adaptive Beamforming....Pages 251-287
Parallel Algorithms for Supercomputers....Pages 289-318
Updating Techniques in Parallel Computation....Pages 319-319
On the Use of the Singular Value Decomposition in Identification and Signal Processing....Pages 321-360
Structured Linear Algebra Problems in Digital Signal Processing....Pages 361-384
Constructing a Unitary Hessenberg Matrix from Spectral Data....Pages 385-395
Correcting Interface Errors Arising from Segmentation in a Parallel Iterative Algorithm....Pages 397-399
Multidimensional Internally Lossless Filters of Fully Recursive Half-Plane Type....Pages 401-411
Rank-One Extensions of the Generalized Hermitian Eigenvalue Problem for Adaptive High Resolution Array Processing....Pages 413-415
A Hybrid Scheme for the Singular Value Decomposition on a Multiprocessor....Pages 417-418
The Weak Stability of Algorithms for Matrix Computations....Pages 419-428
Parallelism in Dynamic Programming and Control....Pages 429-433
Design Issues for Parallel Matrix Algorithms....Pages 435-441
Fast Computation of a Restricted Subset of Eigenpairs of a Varying Hermitian Matrix....Pages 443-455
Parallelization of Toeplitz Solvers....Pages 457-466
Parallel Gaussian Elimination, iPSC/2 Hypercube versus a Transputer Network....Pages 467-476
Snapshots of Mobile Jacobi....Pages 477-484
Computing Generalized Canonical Correlations....Pages 485-488
Introduction to High Resolution Array Spectrum Estimation....Pages 489-494
Modifications of the Normal Equations Method that are Numerically Stable....Pages 495-500
Block Elimination with Iterative Refinement for Bordered Linear Systems....Pages 501-512
The Efficient Calculation of the Eigenvalues, Eigenvectors and Inverses of a Special Class of Brownian Matrices....Pages 513-519
Improvements of Stepsize Control in Numerical Integration....Pages 521-527
A Statistical Evaluation of Inverse Iteration....Pages 529-530
On Underdetermined Systems....Pages 531-540
A chart of numerical methods for structured eigenvalue problems....Pages 541-545
Updating Choleski Factors in Parallel....Pages 547-547
Approximate Inversion of Partially Specified Positive Definite Matrices....Pages 549-557
Nearest “Unstable” Matrix Pencil to a Given Pencil....Pages 559-567
Parallel Recursive Least Squares on a Hypercube Multiprocessor....Pages 569-569
A Divide and Conquer Method for the Unitary Eigenproblem and Applications....Pages 571-577
Utilization of the Matrix Pencil to Extract Poles of a Linear Time-Invariant System....Pages 579-580
Efficient Solution of Minimum Eigen-Problem of Hankel Systems by Conjugate Gradient Algorithm and FFT....Pages 581-585
Progress Towards a Systolic SVD Array Implementation....Pages 587-593
On the Convergence of Cyclic Jacobi Methods....Pages 595-595
Numerically Stable Fast Transversal Filters for Recursive Least-Squares Adaptive Filtering....Pages 597-604
Applications of Analytic Centers....Pages 605-615
Solving Triangular System in Parallel is Accurate....Pages 617-632
Storage Schemes for Parallel Eigenvalue Algorithms....Pages 633-637
Iterative Solution Methods for Large, Sparse Systems of Linear Equations Arising from Tomographic Image Reconstruction....Pages 639-647
The Generalized Total Least Squares Problem : Formulation, Algorithm and Properties....Pages 649-650
Understanding Old Deficiencies in the Conventional Recursive Least-Squares (CRLS) Scheme....Pages 651-660
Algorithms for Optical Computing and their Sensitivity....Pages 661-666
A Constrained Eigenvalue Problem....Pages 667-675
On GR Algorithms for the Eigenvalue Problem....Pages 677-686
Numerical Analysis of Nonlinear Equations in Computer Vision and Robotics....Pages 687-693
A Linear Systolic Array for the Adaptive MVDR Beamformer....Pages 695-704
Solving Band Systems of Linear Equations by Iterative Methods on Vector Machines....Pages 705-711
Back Matter....Pages 713-725
....Pages 727-734

✦ Subjects

Algorithm Analysis and Problem Complexity;Numerical Analysis;Models and Principles;Special Purpose and Application-Based Systems;Communications Engineering, Networks;Mathematical Methods in Physics