Numerical Linear Algebra, Digital Signal Processing and Parallel Algorithms

ISBN-13: 9783642755385 / Angielski / Miękka / 2011 / 729 str.

Gene H. Golub; Paul Van Dooren

Opis

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.

Spis treści

I. Invited Lectures.- The Family of Fast Least Squares Algorithms for Adaptive Filtering.- Adaptive Control Algorithms.- Error Analysis of Least Squares Algorithms.- Parallel Algorithms for Toeplitz Systems.- Parallel Algorithms for Digital Signal Processing.- An Introduction to the Class of Split Levinson Algorithms.- On the Split Approach Based Algorithms for DSP Problems.- Updating and Downdating of Orthogonal Polynomials with Data Fitting Applications.- Parallel Algorithms for Singular Value Problems.- Some Remarks on the Generalised Bareiss and Levinson Algorithms.- Generalized Displacement Structure for Block-Toeplitz, Toeplitz-block, and Toeplitz-derived Matrices.- Fault Tolerant Recursive Least Squares Minimization.- A Systolic Array for Recursive Least Squares Minimisation and Adaptive Beamforming.- Parallel Algorithms for Supercomputers.- Updating Techniques in Parallel Computation.- On the Use of the Singular Value Decomposition in Identification and Signal Processing.- Structured Linear Algebra Problems in Digital Signal Processing.- II. Contributed Lectures.- Constructing a Unitary Hessenberg Matrix from Spectral Data.- Parallel Computation of the Generalized Singular Value Decomposition.- Correcting Interface Errors Arising from Segmentation in a Parallel Iterative Algorithm.- Multidimensional Internally Lossless Filters of Fully Recursive Half-Plane Type.- Rank-One Extensions of the Generalized Hermitian Eigenvalue Problem for Adaptive High Resolution Array Processing.- A Hybrid Scheme for the Singular Value Decomposition on a Multiprocessor.- The Weak Stability of Algorithms for Matrix Computations.- Parallelism in Dynamic Programming and Control.- Design Issues for Parallel Matrix Algorithms.- Fast Computation of a Restricted Subset of Eigenpairs of a Varying Hermitian Matrix.- Parallelization of Toeplitz Solvers.- Parallel Gaussian Elimination, iPSC/2 Hypercube versus a Transputer Network.- Snapshots of Mobile Jacobi.- Computing Generalized Canonical Correlations.- to High Resolution Array Spectrum Estimation.- Modifications of the Normal Equations Method that are Numerically Stable.- Block Elimination with Iterative Refinement for Bordered Linear Systems.- The Efficient Calculation of the Eigenvalues, Eigenvectors and Inverses of a Special Class of Brownian Matrices.- Improvements of Stepsize Control in Numerical Integration.- A Statistical Evaluation of Inverse Iteration.- On Underdetermined Systems.- A chart of numerical methods for structured eigenvalue problems.- Updating Choleski Factors in Parallel.- Approximate Inversion of Partially Specified Positive Definite Matrices.- Nearest “Unstable” Matrix Pencil to a Given Pencil.- Parallel Recursive Least Squares on a Hypercube Multiprocessor.- A Divide and Conquer Method for the Unitary Eigenproblem and Applications.- Utilization of the Matrix Pencil to Extract Poles of a Linear Time-Invariant System.- Efficient Solution of Minimum Eigen-Problem of Hankel Systems by Conjugate Gradient Algorithm and FFT.- Progress Towards a Systolic SVD Array Implementation.- On the Convergence of Cyclic Jacobi Methods.- Numerically Stable Fast Transversal Filters for Recursive Least-Squares Adaptive Filtering.- Applications of Analytic Centers.- Solving Triangular System in Parallel is Accurate.- Storage Schemes for Parallel Eigenvalue Algorithms.- Iterative Solution Methods for Large, Sparse Systems of Linear Equations Arising from Tomographic Image Reconstruction.- The Generalized Total Least Squares Problem: Formulation, Algorithm and Properties.- Understanding Old Deficiencies in the Conventional Recursive Least-Squares (CRLS) Scheme.- Algorithms for Optical Computing and their Sensitivity.- A Constrained Eigenvalue Problem.- On GR Algorithms for the Eigenvalue Problem.- Numerical Analysis of Nonlinear Equations in Computer Vision and Robotics.- A Linear Systolic Array for the Adaptive MVDR Beamformer.- Solving Band Systems of Linear Equations by Iterative Methods on Vector Machines.- List of Participants.