The global Golub-Kahan method and Gauss quadrature for tensor function approximation

This paper is concerned with Krylov subspace methods based on the tensor t-product for  computing certain quantities associated with generalized third-order tensor functions. We use the tensor t-product and define the tensor global Golub-Kahan bidiagonalization process for approximating tensor funct...

Full description

Saved in:
Bibliographic Details
Published in:Numerical algorithms 2023, Vol.92 (1), p.5-34
Main Authors: Bentbib, A. H., Ghomari, M. El, Jbilou, K., Reichel, L.
Format: Article
Language:English
Subjects:
Algebra
Algorithms
Approximation
Computer Science
Decomposition
Fourier transforms
Mathematical analysis
Mathematics
Methods
Numeric Computing
Numerical Analysis
Original Paper
Quadratures
Subspace methods
Tensors
Theory of Computation
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:This paper is concerned with Krylov subspace methods based on the tensor t-product for  computing certain quantities associated with generalized third-order tensor functions. We use the tensor t-product and define the tensor global Golub-Kahan bidiagonalization process for approximating tensor functions. Pairs of Gauss and Gauss-Radau quadrature rules are applied to determine the desired quantities with error bounds. An application to the computation of the tensor nuclear norm is presented and illustrates the effectiveness of the proposed methods.
ISSN:1017-1398
1572-9265
DOI:10.1007/s11075-022-01392-x