Gaussian quadrature for matrix valued functions on the real line
type: Item
instance of: scholarly article
title: Gaussian quadrature for matrix valued functions on the real line
zbMATH Open document ID: 0876.65011
DOI: 10.1016/0377-0427(95)00124-7
author: Ann Sinap
published in: Journal of Computational and Applied Mathematics
publication date: 1996-07-15T00:00:00Z
review text: The author implements the Gaussian quadrature algorithm for matrix-valued functions on a multiprocessor SP1 based on RISC-processors. He gives a formula to determine the quadrature weights using the eigenvalues and components of the normalized eigenvectors of a symmetric block tridiagonal matrix. Because the elements of the main and first subdiagonal are the recursion coefficients of the corresponding orthonormal matrix polynomials, the block version of the modified Chebyshev algorithm to compute these recursion coefficients from the modified moments can be constructed.
Mathematics Subject Classification ID: 65D32
Mathematics Subject Classification ID: 65Y05
Mathematics Subject Classification ID: 42C05
Mathematics Subject Classification ID: 41A55
Mathematics Subject Classification ID: 41A63
zbMATH DE Number: 903587
zbMATH Keywords: parallel computation
zbMATH Keywords: Gaussian quadrature algorithm
zbMATH Keywords: matrix-valued functions
zbMATH Keywords: orthonormal matrix polynomials
zbMATH Keywords: Chebyshev algorithm
reviewed by: Carmen Simerská
describes a project that uses: BRENT
MaRDI profile type: Publication
full work available at URL: 0377-0427(95)00124-7
OpenAlex ID: W2002030371
cites work: Divide and conquer algorithms for the bandsymmetric eigenvalue problem
cites work: On the Spectral Decomposition of Hermitian Matrices Modified by Low Rank Perturbations with Applications
cites work: ON A BLOCK IMPLEMENTATION OF HESSENBERG MULTISHIFT QR ITERATION
cites work: A Parallel QR Factorization Algorithm with Controlled Local Pivoting
cites work: Q5657612
cites work: Analysis of the Diagonal Pivoting Method
cites work: Some Stable Methods for Calculating Inertia and Solving Symmetric Linear Systems
cites work: Rank-one modification of the symmetric eigenproblem
cites work: Direct Methods for Solving Symmetric Indefinite Systems of Linear Equations
cites work: A Divide and Conquer method for the symmetric tridiagonal eigenproblem
cites work: A Fully Parallel Algorithm for the Symmetric Eigenvalue Problem
cites work: Reduction to condensed form for the eigenvalue problem on distributed memory architectures
cites work: Q4134790
cites work: On Generating Orthogonal Polynomials
cites work: Orthogonal polynomials - Constructive theory and applications
cites work: Q3473613
cites work: Scattering theory and matrix orthogonal polynomials on the real line
cites work: Q3939931
cites work: A parallel algorithm for the dense symmetric eigenvalue problem on a transputer array
cites work: The generalized Householder transformation and sparse matrices
cites work: Fundamental aspects of the representation theory of Hermitian operators with deficiency index (𝑚,𝑚)
cites work: A Parallel Algorithm for Reducing Symmetric Banded Matrices to Tridiagonal Form
cites work: Implicit Shifting in the QR and Related Algorithms
cites work: A new efficient parallelization strategy for the \(QR\) algorithm
cites work: Block Reflectors: Theory and Computation
cites work: Polynomial interpolation and Gaussian quadrature for matrix-valued functions
cites work: Orthogonal matrix polynomials and applications
description: scientific article; zbMATH DE number 903587