Linear Algebra for Large Scale and Real-Time Applications

✍ Scribed by P. E. Bjørstad, J. Cook (auth.), Marc S. Moonen, Gene H. Golub, Bart L. R. De Moor (eds.)

• Publisher: Springer Netherlands
• Year: 1993
• Tongue: English
• Leaves: 434
• Series: NATO ASI Series 232
• Edition: 1
• Category: Library

✦ Synopsis

In recent years there has been great interest in large scale and real-time matrix computations; these computations arise in a variety of fields, such as computer graphics, imaging, speech and image processing, telecommunication, biomedical signal processing, optimization and so on. This volume, which is an outgrowth of a NATO ASI, held at Leuven, Belgium, August 1992, gives an account of recent research advances in numerical techniques used in large scale and real-time computations and their implementation on high performance computers.
For anyone interested in any of these disciplines, this collection of papers is invaluable and provides state-of-the-art expositions as well as new and important trends and directions for the future, motivated and illustrated by a wealth of scientific and engineering applications.

✦ Table of Contents

Front Matter....Pages i-xi
Front Matter....Pages 1-1
Large Scale Structural Analysis on Massively Parallel Computers....Pages 3-11
Data-Parallel BLAS as a Basis for LAPACK on Massively Parallel Computers....Pages 13-20
Large-Scale Nonlinear Constrained Optimization....Pages 21-48
Trading off Parallelism and Numerical Stability....Pages 49-68
Subband Filtering: Cordic Modulation and Systolic Quadrature Mirror Filter Tree....Pages 69-89
A Parallel Image Rendering Algorithm and Architecture Based on Ray Tracing and Radiosity Shading....Pages 91-108
Reduction and Approximation of Linear Computational Circuits....Pages 109-135
The Look-Ahead Lanczos Process for Large Nonsymmetric Matrices and Related Algorithms....Pages 137-163
Case Studies of Real-Time Processing in Robotics....Pages 165-182
Adaptive Signal Processing with Emphasis on QRD-Least Squares Lattice....Pages 183-194
A Direct Method for Reordering Eigenvalues in the Generalized Real Schur form of a Regular Matrix Pair ( A, B )....Pages 195-218
Block Shift Invariance and Efficient System Identification Algorithms....Pages 219-229
Computing the Singular Value Decomposition on a Fat-Tree Architecture....Pages 231-240
A New Matrix Decomposition for Signal Processing....Pages 241-247
The Linear Algebra of Perfect Reconstruction Filtering....Pages 249-274
Determining Rank in the Presence of Error....Pages 275-291
Approximation with Kronecker Products....Pages 293-314
Some Linear Algebra Issues in Large-Scale Optimization....Pages 315-337
Front Matter....Pages 339-339
Direct and Inverse Unitary Eigenproblems in Signal Processing: An Overview....Pages 341-343
Block Implementations of the Symmetric QR and Jacobi Algorithms....Pages 345-346
Front Matter....Pages 339-339
Linear Algebra for Large-Scale Information Retrieval Applications....Pages 347-348
Matched Filter vs. Least-Squares Approximation....Pages 349-350
Reordering Diagonal Blocks in Real Schur Form....Pages 351-352
Placing Zeroes and the Kronecker Canonical Form....Pages 353-354
Analysis of the Recursive Least Squares Lattice Algorithm....Pages 355-356
Adaptive Chebyshev Iteration Based on Modified Moments....Pages 357-358
Continuous Realization Methods and their Applications....Pages 359-360
Asymptotic Behavior of Orthogonal Polynomials....Pages 361-362
CADCS and Parallel Computing....Pages 363-364
Eigenvalue Roulette and Random Test Matrices....Pages 365-368
On Numerical Methods for Unitary Eigenvalue Problems....Pages 369-370
Accurate Singular Values and Differential QD Algorithms....Pages 371-373
Orthogonal Projection and Total Least Squares....Pages 375-376
Gauss Quadratures Associated with the Arnoldi Process and the Lanczos Algorithm....Pages 377-380
An Implementation of the QMR Method Based on Coupled Two-Term Recurrences....Pages 381-384
Computationally Efficient Homotopies for the H 2 Model order Reduction Problem....Pages 385-386
A Fast Algorithm for QR Decomposition of Toeplitz Matrices....Pages 387-388
Unitary Hessenberg Methods for Toeplitz Approximations and Applications....Pages 389-390
Perturbation Theory and Backward Error for AX - XB = C ....Pages 391-391
Fast Transforms and Elliptic Problems....Pages 393-394
Front Matter....Pages 339-339
An Interior-Point Method for Minimizing the Maximum Eigenvalue of a Linear Combination of Matrices....Pages 395-396
The Lattice-Ladder with Generalized Forgetting....Pages 397-398
Solving a Least Squares Problem with Boundary Constraints....Pages 399-400
Estimating the Extremal Eigenvalues and Condition Number by the Lanczos Algorithm with a Random Start....Pages 401-402
A Generalized ADI Iterative Method....Pages 403-404
Quaternions and the Symmetric Eigenvalue Problem....Pages 405-406
Application of Gauss-Seidel Iteration to the RLS Algorithm....Pages 407-408
Ranks of Submatrices of a Matrix and Its Inverse....Pages 409-410
A QRD-Based Least-Squares Algorithm for Multipulse Antenna Array Signal Processing....Pages 411-412
On Displacement Structures for Covariance Matrices and Lossless Functions....Pages 413-414
Application of Vector Extrapolation and Conjugate Gradient Type Methods to the Semiconductor Device Problem....Pages 415-416
Accurate Symmetric Eigenreduction by a Jacobi Method....Pages 417-418
The Order-Recursive Chandrasekhar Equations for Fast Square-Root Kalman Filtering....Pages 419-420
Hybrid Iterative Methods Based on Faber Polynomials....Pages 421-422
Aspects of Implementing a ‘C’ Matrix Library....Pages 423-424
Intermediate Fill-In in Sparse QR Decomposition....Pages 425-426
Shifting Strategies for the Parallel QR Algorithm....Pages 427-428
Back Matter....Pages 429-437

✦ Subjects

Mathematical Modeling and Industrial Mathematics; Numeric Computing; Computer Science, general; Systems Theory, Control