Lower estimates on the condition number of a Toeplitz sinc matrix and related questions

Authors : Ludwig KOHAUPT, Yan WU

Pages : 168-182

Doi:10.33205/cma.1142905

View : 42 | Download : 7

Publication Date : 2022-09-15

Article Type : Research Paper

Abstract :As one new result, for a symmetric Toeplitz $ \operatorname{sinc} $ $n \times n$-matrix $Ainsert ignore into journalissuearticles values(t);$ depending on a parameter $t$, lower estimates insert ignore into journalissuearticles values(tending to infinity as t vanishes); on the pertinent condition number are derived. A further important finding is that prior to improving the obtained lower estimates it seems to be more important to determine the lower bound on the parameter $t$ such that the smallest eigenvalue $\mu_ninsert ignore into journalissuearticles values(t);$ of $Ainsert ignore into journalissuearticles values(t);$ can be reliably computed since this is a precondition for determining a reliable value for the condition number of the Toeplitz $ \operatorname{sinc} $ matrix. The style of the paper is expository in order to address a large readership.
Keywords : Condition number, eigenvalues and eigenvectors, inverse power method, power method, Toeplitz sinc matrix

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