On Parabolic and Elliptic Spectral Dichotomy
Alexander N. Malyshev, Miloud Sadkane · SIAM Journal on Matrix Analysis and Applications · 1997
We discuss two spectral dichotomy techniques: one for computing an invariant subspace of a nonsymmetric matrix associated with the eigenvalues inside and outside a given parabola; another one for computing a right deflating subspace of a regular matrix pencil associated with the eigenvalues inside and outside a given ellipse. The techniques use matrices of twice the order of the original matrices on which the spectral dichotomy by the unit circle and by the imaginary axis apply efficiently. We prove the equivalence between the condition number of the original problems and that of the transformed ones.