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SLASD4(1) LAPACK auxiliary routine (version 3.2) SLASD4(1)

NAME

SLASD4 - subroutine compute the square root of the I-th updated eigenvalue of a positive symmetric rank-one modification to a positive diagonal matrix whose entries are given as the squares of the corresponding entries in the array d, and that 0 <= D(i) < D(j) for i < j and that RHO > 0

SYNOPSIS

N, I, D, Z, DELTA, RHO, SIGMA, WORK, INFO )

INTEGER I, INFO, N REAL RHO, SIGMA REAL D( * ), DELTA( * ), WORK( * ), Z( * )

PURPOSE

This subroutine computes the square root of the I-th updated eigenvalue of a positive symmetric rank-one modification to a positive diagonal matrix whose entries are given as the squares of the corresponding entries in the array d, and that no loss in generality. The rank-one modified system is thus
diag( D ) * diag( D ) + RHO * Z * Z_transpose.
where we assume the Euclidean norm of Z is 1.
The method consists of approximating the rational functions in the secular equation by simpler interpolating rational functions.

ARGUMENTS

The length of all arrays.
The index of the eigenvalue to be computed. 1 <= I <= N.
The original eigenvalues. It is assumed that they are in order, 0 <= D(I) < D(J) for I < J.
The components of the updating vector.
If N .ne. 1, DELTA contains (D(j) - sigma_I) in its j-th component. If N = 1, then DELTA(1) = 1. The vector DELTA contains the information necessary to construct the (singular) eigenvectors.
The scalar in the symmetric updating formula.
The computed sigma_I, the I-th updated eigenvalue.
If N .ne. 1, WORK contains (D(j) + sigma_I) in its j-th component. If N = 1, then WORK( 1 ) = 1.
= 0: successful exit
> 0: if INFO = 1, the updating process failed.

PARAMETERS

Logical variable ORGATI (origin-at-i?) is used for distinguishing whether D(i) or D(i+1) is treated as the origin. ORGATI = .true. origin at i ORGATI = .false. origin at i+1 Logical variable SWTCH3 (switch-for-3-poles?) is for noting if we are working with THREE poles! MAXIT is the maximum number of iterations allowed for each eigenvalue. Further Details =============== Based on contributions by Ren-Cang Li, Computer Science Division, University of California at Berkeley, USA

November 2008 LAPACK auxiliary routine (version 3.2)