Algorithm 918: specdicho: A MATLAB Program for the Spectral Dichotomy of Regular Matrix Pencils

摘要

Given a regular matrix pencil λB - A and a positively oriented contour y in the complex plane, the spectral dichotomy methods applied to λB-A and y consist in determining whether λB - A possesses eigenvalues on or in a neighborhood of y. When no such eigenvalues exist, these methods compute iteratively the spectral projector P onto the right deflating subspace of λB - A associated with the eigenvalues inside/outside y. The computation of the projector is accompanied by the spectral norm ||H|| of a Hermitian positive definite matrix H called the dichotomy condition number, which indicates the numerical quality of the spectral projector P. The smaller ||H|| is, the better this quality. This article presents a MATLAB program (specdicho) implementing the main types of spectral dichotomy where y is a circle, an ellipse, the imaginary axis or a parabola.