Algorithm 918

Abstract

Given a regular matrix pencil λ B -- A and a positively oriented contour γ in the complex plane, the spectral dichotomy methods applied to λ B -- A and γ consist in determining whether λ B -- 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 λ B -- 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.