A Note on the Superoptimal Matrix Algebra Operators

1 January 2002

journal article
research article
Published by Taylor & Francis in Linear and Multilinear Algebra

Vol. 50 (4) , 343-372
https://doi.org/10.1080/0308108021000049301

Abstract

We study the superoptimal Frobenius operators in several matrix vector spaces and in particular in the circulant algebra, by emphasizing both the algebraic and geometric properties. More specifically we prove a series of "negative" results that explain why this approximation procedure is not competitive with the optimal Frobenius approximation, although it could be used for regularization purposes.

Keywords

This publication has 35 references indexed in Scilit:

Superlinear Convergence of Conjugate Gradients
SIAM Journal on Numerical Analysis, 2001
Introduction to Large Truncated Toeplitz Matrices
Published by Springer Nature ,1999
Solution of Toeplitz normal equations by sine transform based preconditioning
Linear Algebra and its Applications, 1998
Introduction to Inverse Problems in Imaging
Published by Taylor & Francis ,1998
Conjugate Gradient Methods for Toeplitz Systems
SIAM Review, 1996
Analysis of Preconditioning Techniques for Ill-Conditioned Toeplitz Matrices
SIAM Journal on Scientific Computing, 1995
On a Matrix Algebra Related to the Discrete Hartley Transform
SIAM Journal on Matrix Analysis and Applications, 1993
C. G. preconditioning for Toeplitz matrices
Computers & Mathematics with Applications, 1993
Toeplitz Preconditioners for Toeplitz Systems with Nonnegative Generating Functions
IMA Journal of Numerical Analysis, 1991
An Optimal Circulant Preconditioner for Toeplitz Systems
SIAM Journal on Scientific and Statistical Computing, 1988