Bounds for the smallest singular value of a Jordan block with an application to eigenvalue perturbation
The paper brings some new bounds for the smallest singular value of Jordan canonical blocks. The inequalities are given in terms of the magnitude of the smallest singular value \((s)\) and the size of the matrix block \((m)\). Three cases are considered: either \(s\) is greater, equal or smaller (but positive) than \(m/(m + 1)\). These bounds are applied to eigenvalue perturbation, giving lower bounds for more general matrices (e.g. Hessenberg matrices).
scientific article; zbMATH DE number 553982