slaic1(3)

NAME

SLAIC1 - applie one step of incremental condition estima

tion in its simplest version

SYNOPSIS

SUBROUTINE SLAIC1( JOB, J, X, SEST, W, GAMMA, SESTPR, S, C
)
    INTEGER        J, JOB
    REAL           C, GAMMA, S, SEST, SESTPR
    REAL           W( J ), X( J )

PURPOSE

SLAIC1 applies one step of incremental condition estima

tion in its simplest version: Let x, twonorm(x) = 1, be an ap

proximate singular vector of an j-by-j lower triangular matrix L,

such that

twonorm(L*x) = sest

Then SLAIC1 computes sestpr, s, c such that
the vector

[ s*x ]

xhat = [ c ]

is an approximate singular vector of

[ L 0 ]

Lhat = [ w' gamma ]

in the sense that

twonorm(Lhat*xhat) = sestpr.

Depending on JOB, an estimate for the largest or smallest

singular value is computed.

Note that [s c]' and sestpr**2 is an eigenpair of the sys

tem

diag(sest*sest, 0) + [alpha gamma] * [ alpha ]

[ gamma ]

where alpha = x'*w.

ARGUMENTS

JOB (input) INTEGER

= 1: an estimate for the largest singular value is

computed.
= 2: an estimate for the smallest singular value

is computed.

J (input) INTEGER

Length of X and W

X (input) REAL array, dimension (J)

The j-vector x.

SEST (input) REAL

Estimated singular value of j by j matrix L

W (input) REAL array, dimension (J)

The j-vector w.

GAMMA (input) REAL

The diagonal element gamma.

SESTPR (output) REAL

Estimated singular value of (j+1) by (j+1) matrix

Lhat.

S (output) REAL

Sine needed in forming xhat.

C (output) REAL

Cosine needed in forming xhat.

LAPACK version 3.0 15 June 2000

SLAIC1(3)