Eigenvalues and eigenvectors of symmetric matrices, case 320

A FORTRAN IV subroutine has .been written which, when used in conjunction with the subroutine TRIDMX. in the UNIVAC 1108 MATH-PACK, will find the eigenvalues, and a set of orthogonal eigenvectors, for any real symmetric matrix.*The subroutine applies the QR algoriA-.hmto a symmetric tri-diagural matrix.This algorithm finds a sequence of matrices, which are orthogonally similar to the original matrix, and which converges to a diagonal matrix.The product of the similarity transformations converges to the matrix of eigenvectors; hence the algorithm produces orthogonal eigenvectors, even when some eigenvalues are multiple.Also included is a subroutine which uses the output of TRIDMX to transform the eigenvectors of the tri-diagonal matrix into the eigenvectors of the original matrix.* The subroutine TRIDMX uses Householders' method to transform a symmetric matrix into tri-diagonal form. I N69ma39(32A