specdicho

Algorithm 918: specdicho: A MATLAB Program for the Spectral Dichotomy of Regular Matrix Pencils. Given a regular matrix pencil λB -- A and a positively oriented contour γ in the complex plane, the spectral dichotomy methods applied to λB -- A and γ consist in determining whether λB -- A possesses eigenvalues on or in a neighborhood of γ. 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 γ. 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 γ is a circle, an ellipse, the imaginary axis or a parabola.

This software is also peer reviewed by journal TOMS.