Algorithm 710: FORTRAN subroutines for computing the eigenvalues and eigenvectors of a general matrix by reduction to general tridiagonal form

Abstract

This paper describes programs to reduce a nonsymmetric matrix to tridiagonal form, to compute the eigenvalues of the tridiagonal matrix, to improve the accuracy of an eigenvalue, and to compute the corresponding eigenvector. The intended purpose of the software is to find a few eigenpairs of a dense nonsymmetric matrix faster and more accurately than previous methods. The performance and accuracy of the new routines are compared to two EISPACK paths: RG and HQR-INVIT. The results show that the new routines are more accurate and also faster if less than 20 percent of the eigenpairs are needed.