Gamma-matrices: a new class of simultaneously diagonalizable matrices
Numerical Analysis
2021-07-14 v1 Numerical Analysis
Abstract
In order to precondition Toeplitz systems, we present a new class of simultaneously diagonalizable real matrices, the Gamma-matrices, which include both symmetric circulant matrices and a subclass of the set of all reverse circulant matrices. We define some algorithms for fast computation of the product between a Gamma-matrix and a real vector and between two Gamma-matrices. Moreover, we illustrate a technique of approximating a real symmetric Toeplitz matrix by a Gamma-matrix, and we show that the eigenvalues of the preconditioned matrix are clustered around zero with the exception of at most a finite number of terms.
Cite
@article{arxiv.2107.05890,
title = {Gamma-matrices: a new class of simultaneously diagonalizable matrices},
author = {Antonio Boccuto and Ivan Gerace and Valentina Giorgetti and Federico Greco},
journal= {arXiv preprint arXiv:2107.05890},
year = {2021}
}