Solution of Eigenvalue problems with approximately known Eigenvectors
It is often desired to solve eigenvalue problems of the type (A - &lgr;1)C = 0 or (A - &lgr;B)C = 0 repeatedly for similar values of the matrix elements Aij, where A and B are Hermitean or real symmetric matrices. Among the various methods to find all eigenvalues and eigenvectors, Jacobi's method of two-dimensional rotations [1] has been very popular for its numerical stability, although it is comparatively time-consuming. The purpose of this note is to show how existing subroutines can be used to reduce substantially the computing time, if approximate eigenvectors are known from the previous solution of a similar problem.