Algorithm 918: specdicho: A MATLAB Program for the Spectral Dichotomy of Regular Matrix Pencils
Given a regular matrix pencil lambda B - A and a positively oriented contour gamma in the complex plane, the spectral dichotomy methods applied to lambda B - A and gamma consist in determining whether lambda B - A possesses eigenvalues on or in a neighborhood of gamma. When no such eigenvalues exist, these methods compute iteratively the spectral projector P onto the right deflating subspace of lambda B - A associated with the eigenvalues inside/outside gamma. The computation of the projector is accompanied by the spectral norm parallel to H parallel to of a Hermitian positive definite matrix H called the dichotomy condition number, which indicates the numerical quality of the spectral projector P. The smaller parallel to H parallel to is, the better this quality. This article presents a MATLAB program (specdicho) implementing the main types of spectral dichotomy where gamma is a circle, an ellipse, the imaginary axis or a parabola.
algorithms spectral dichotomy regular matrix pencil spectral projector documentation invariant subspace