RATIONAL KRYLOV FOR REAL PENCILS WITH COMPLEX EIGENVALUES

Abstract

A rational Krylov algorithm for eigenvalue computation is described. It is usable on a real matrix pencil with complex eigenvalues and builds up a real basis. The main purpose is to get real reduced models of a real linear dynamic system. Two variants are described, one where two real vectors are added to the Krylov space in each step and another where just one real vector is added in each step.

Results are reported from one small example that has been used earlier and where the solution is known, and one more realistic example, a linear descriptor system from a computational fluid dynamics application.