Projection Method for Eigenvalue Problems of Linear Nonsquare Matrix Pencils

Eigensolvers involving complex moments can determine all the eigenvalues in a given region plane and corresponding eigenvectors of regular linear matrix pencil. The moment acts as filter for extracting eigencomponents interest from random vectors or matrices. This study extends projection method eigenproblems to singular nonsquare case, thus replacing standard inverse resolvent with pseudoinverse. extended involves by contour integrals generalized resolvents associated We establish conditions such that gives finite prescribed plane. In numerical computations, are approximated using quadratures. primary cost lies solutions least squares problems arise quadrature points, they be readily parallelized practice. Numerical experiments on large pencils illustrate this method. new is more robust efficient than previous methods, based experimental results, it conjectured settings. Notably, proposed does not fail cases pairs extremely close eigenvalues, overcomes issue problem size.