Computation of selected eigenvalues of generalized eigenvalue problems

Abstract

The Arnoldi (1951) and Lanczos (1950) iterative algorithms are used to obtain a few selected eigenvalues of the generalized eigenvalue problem A(x) = lambdaB(x), where A and B are n x n nonsymmetric banded complex matrices. A shift-and-invert strategy is used to increase the rate of convergence toward the desired eigenvalues, and the two approaches are evaluated in view of their performance in a model problem concerning the linear stability of compressible boundary layers. A general scheme for computing the eigenvalues that lie within a 'box' in the complex plane is presented.