TQLRAT(3)

SYNOPSIS
SUBROUTINE TQLRAT (N, D, E2, IERR)

NAME
tqlrat - Compute the eigenvalues of symmetric tridiagonal matrix using a rational variant of the QL method.

LIBRARY
SLATEC (EISPACK)

CATEGORY
D4A5, D4C2A

TYPE
SINGLE PRECISION (TQLRAT-S)

KEYWORDS
EIGENVALUES OF A SYMMETRIC TRIDIAGONAL MATRIX, EISPACK, QL METHOD

AUTHOR
Smith, B. T., et al.

DESCRIPTION
This subroutine is a translation of the ALGOL procedure TQLRAT. This subroutine finds the eigenvalues of a SYMMETRIC TRIDIAGONAL matrix by the rational QL method. On Input N is the order of the matrix. N is an INTEGER variable. D contains the diagonal elements of the symmetric tridiagonal matrix. D is a one-dimensional REAL array, dimensioned D(N). E2 contains the squares of the subdiagonal elements of the symmetric tridiagonal matrix in its last N-1 positions. E2(1) is arbitrary. E2 is a one-dimensional REAL array, dimensioned E2(N). On Output D contains the eigenvalues in ascending order. If an error exit is made, the eigenvalues are correct and ordered for indices 1, 2, ..., IERR-1, but may not be the smallest eigenvalues. E2 has been destroyed. IERR is an INTEGER flag set to Zero for normal return, J if the J-th eigenvalue has not been determined after 30 iterations. Calls PYTHAG(A,B) for sqrt(A**2 + B**2). Questions and comments should be directed to B. S. Garbow, APPLIED MATHEMATICS DIVISION, ARGONNE NATIONAL LABORATORY ------------------------------------------------------------------

REFERENCES
B. T. Smith, J. M. Boyle, J. J. Dongarra, B. S. Garbow, Y. Ikebe, V. C. Klema and C. B. Moler, Matrix Eigen- system Routines - EISPACK Guide, Springer-Verlag, 1976. C. H. Reinsch, Eigenvalues of a real, symmetric, tri- diagonal matrix, Algorithm 464, Communications of the ACM 16, 11 (November 1973), pp. 689.

ROUTINES CALLED
PYTHAG, R1MACH

REVISION HISTORY (YYMMDD)
760101 DATE WRITTEN
890831 Modified array declarations. (WRB)
890831 REVISION DATE from Version 3.2
891214 Prologue converted to Version 4.0 format. (BAB)
920501 Reformatted the REFERENCES section. (WRB)