Positive definite Toeplitz matrices, the Arnoldi process for isometric operators, and Gaussian quadrature on the unit circle
type: Item
instance of: scholarly article
title: Positive definite Toeplitz matrices, the Arnoldi process for isometric operators, and Gaussian quadrature on the unit circle
zbMATH Open document ID: 0777.65013
DOI: 10.1016/0377-0427(93)90294-L
author: W. B. Gragg
published in: Journal of Computational and Applied Mathematics
publication date: 1993-01-01T00:00:00Z
review text: It is shown that the Levinson algorithm for the inverse Cholesky factorization of positive definite Toeplitz matrices is a special case of a more general method. An efficient implementation of the Arnoldi process for isometric operators is given. A Gaussian quadrature on the unit circle is derived.
reviewed by: S.Filippi
Mathematics Subject Classification ID: 65F05
Mathematics Subject Classification ID: 65D32
Mathematics Subject Classification ID: 41A55
Mathematics Subject Classification ID: 30E10
Mathematics Subject Classification ID: 65E05
zbMATH DE Number: 219119
zbMATH Keywords: Levinson algorithm
zbMATH Keywords: inverse Cholesky factorization
zbMATH Keywords: positive definite Toeplitz matrices
zbMATH Keywords: Arnoldi process
zbMATH Keywords: isometric operators
zbMATH Keywords: Gaussian quadrature
MaRDI profile type: Publication
cites work: Q5601153
cites work: The principle of minimized iterations in the solution of the matrix eigenvalue problem
cites work: Discrete and continuous boundary problems
cites work: Moments and characteristic roots
cites work: Rank-one modification of the symmetric eigenproblem
cites work: The Numerical Stability of the Levinson-Durbin Algorithm for Toeplitz Systems of Equations
cites work: A General Orthogonalization Technique with Applications to Time Series Analysis and Signal Processing
cites work: Restrictions of Normal Operators, Padé Approximation and Autoregressive Time Series
cites work: Matrix interpretations and applications of the continued fraction algorithm
cites work: On fast computation of superdiagonal Padé fractions
cites work: Separation theorems for normalizable matrices
cites work: Moments and characteristic roots. II
cites work: Q3664266
cites work: Q3968381
cites work: Bestimmung der Eigenwerte orthogonaler Matrizen
Recommended article: Q3217521
Recommended article: Toeplitz determinants and positive semidefiniteness
Recommended article: Quasi-positive definite operators and matrices
Recommended article: Q3479058
Recommended article: On some properties of positive definite Toeplitz matrices and their possible applications
Recommended article: Some limit relations for multidimensional positive-definite Toeplitz matrices
Recommended article: Isometries on positive definite operators with unit Fuglede-Kadison determinant
Recommended article: Bounds on the size of nonnegative definite circulant embeddings of positive definite Toeplitz matrices
Recommended article: Q4615518
Recommended article: On the Relation Between Positive Definite Functions and Generalized Toeplitz Kernels
description: scientific article; zbMATH DE number 219119