Numerical Linear Algebra, Digital Signal Processing and Parallel Algorithms

This Advanced Study Institute volume is a collection of invited tutorials and contributed research papers covering the interdisciplinary field of numerical linear algebra, digital signal processing, and parallel algorithms.

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.