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.TH DLAIC1 l "15 June 2000" "LAPACK version 3.0" ")"
.SH NAME
DLAIC1 - applie one step of incremental condition estimation in its simplest version
.SH SYNOPSIS
.TP 19
SUBROUTINE DLAIC1(
JOB, J, X, SEST, W, GAMMA, SESTPR, S, C )
.TP 19
.ti +4
INTEGER
J, JOB
.TP 19
.ti +4
DOUBLE
PRECISION C, GAMMA, S, SEST, SESTPR
.TP 19
.ti +4
DOUBLE
PRECISION W( J ), X( J )
.SH PURPOSE
DLAIC1 applies one step of incremental condition estimation in its simplest version:
Let x, twonorm(x) = 1, be an approximate singular vector of an j-by-j
lower triangular matrix L, such that
.br
twonorm(L*x) = sest
.br
Then DLAIC1 computes sestpr, s, c such that
.br
the vector
.br
[ s*x ]
.br
xhat = [ c ]
.br
is an approximate singular vector of
.br
[ L 0 ]
.br
Lhat = [ w' gamma ]
.br
in the sense that
.br
twonorm(Lhat*xhat) = sestpr.
.br
Depending on JOB, an estimate for the largest or smallest singular
value is computed.
.br
Note that [s c]' and sestpr**2 is an eigenpair of the system
diag(sest*sest, 0) + [alpha gamma] * [ alpha ]
.br
[ gamma ]
.br
where alpha = x'*w.
.br
.SH ARGUMENTS
.TP 8
JOB (input) INTEGER
= 1: an estimate for the largest singular value is computed.
.br
= 2: an estimate for the smallest singular value is computed.
.TP 8
J (input) INTEGER
Length of X and W
.TP 8
X (input) DOUBLE PRECISION array, dimension (J)
The j-vector x.
.TP 8
SEST (input) DOUBLE PRECISION
Estimated singular value of j by j matrix L
.TP 8
W (input) DOUBLE PRECISION array, dimension (J)
The j-vector w.
.TP 8
GAMMA (input) DOUBLE PRECISION
The diagonal element gamma.
.TP 8
SEDTPR (output) DOUBLE PRECISION
Estimated singular value of (j+1) by (j+1) matrix Lhat.
.TP 8
S (output) DOUBLE PRECISION
Sine needed in forming xhat.
.TP 8
C (output) DOUBLE PRECISION
Cosine needed in forming xhat.
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