Unitary orthogonalization processes
type: Item
instance of: scholarly article
title: Unitary orthogonalization processes
zbMATH Open document ID: 0903.65048
DOI: 10.1016/S0377-0427(97)00165-9
author: David S. Watkins
published in: Journal of Computational and Applied Mathematics
publication date: 1999-01-05T00:00:00Z
review text: Let \({\mathcal H}\) be a complex separable Hilbert space over \(\mathbb{C}\) with an inner product \((.,.)\), \(U:{\mathcal H}\to {\mathcal H}\) be a unitary operator (i.e. \((Ux,Uy)= (x, y)\) for all \(x,y\in {\mathcal H}\)) and \(0\neq h\in{\mathcal H}\). The authors consider a two-sided orthogonalization process for the bilateral Krylov sequence \(\{U^kh\}^\infty_{k=-\infty}\), which is equivalent to the Gragg's isometric Arnoldi process. The connection of this process to other classical algorithms of signal processing is also discussed.
Mathematics Subject Classification ID: 65J05
Mathematics Subject Classification ID: 65F25
Mathematics Subject Classification ID: 46C05
zbMATH DE Number: 1115941
zbMATH Keywords: Hilbert space
zbMATH Keywords: orthogonalization
zbMATH Keywords: Krylov sequence
zbMATH Keywords: Gragg's isometric Arnoldi process
zbMATH Keywords: algorithms
zbMATH Keywords: signal processing
reviewed by: Mihail M. Konstantinov
MaRDI profile type: Publication
cites work: A General Orthogonalization Technique with Applications to Time Series Analysis and Signal Processing
cites work: The Fitting of Time-Series Models
cites work: Q4868403
cites work: Q3359644
cites work: Q3217521
cites work: Positive definite Toeplitz matrices, the Arnoldi process for isometric operators, and Gaussian quadrature on the unit circle
cites work: What Does the Spectral Theorem Say?
cites work: Maximum entropy and the moment problem
cites work: A class of all-zero lattice digital filters: Properties and applications
cites work: Q4061445
cites work: Q3800532
cites work: Some Perspectives on the Eigenvalue Problem
cites work: Q5794082
full work available at URL: s0377-0427(97)00165-9
OpenAlex ID: W1996288116
Recommended article: On counter orthogonalization processes
Recommended article: Optimal orthogonalization processes
Recommended article: Unitary approximation
Recommended article: Orthogonal dualities of Markov processes and unitary symmetries
Recommended article: Unitary processes with independent increments and representations of Hilbert tensor algebras
Recommended article: Unitary Integrators and Applications to Continuous Orthonormalization Techniques
Recommended article: UNITARY PROPAGATION OF OPERATOR DATA
Recommended article: Matrices of unitary moments
Recommended article: Uncorrelatedness and orthogonality for vector-valued processes
Recommended article: A process of orthogonalization in the Gauss space
description: scientific article; zbMATH DE number 1115941