Efficient eigenvector sensitivities by a new procedure based on Lanczos vectors

Abstract

A new procedure, based on the use of Lanczos vectors, for the efficient computation of eigenvector sensitivities to changes in system parameters is presented. The method is based on a matrix reduction that uses the same Lanczos vectors as those used to obtain the original eigenvectors. Thus, the equation systems that are solved can be greatly reduced from the original matrix sizes. An explanation of why the method is most accurate for the lowest eigenvectors' derivatives is offered. Numerical results for two modest-sized examples are supplied, from which trends in the method's accuracy are suggested.