Improving eigenvalue bounds using extra bounds
In previous papers, the authors (with others) have obtained very good bounds for various functions of the eigenvalues of an \(n\times n\) complex matrix with real eigenvalues \(\lambda_ 1\geq \lambda_ 2\geq...\geq \lambda_ n\)- in fact the best bounds when using only n, tr A and tr \(A^ 2\). In this paper, with A Hermitian, the authors use besides the information given by the diagonal elements and present a program to obtain the best possible upper bound for \(\lambda_ k\) and the best lower bound for \(\lambda_{k+1}\), given n, tr A, tr \(A^ 2\) and the ordered diagonal elements. This program is illustrated by several examples. Other bounds are obtained invoking some matrix norms.
scientific article; zbMATH DE number 3916479