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CLAIC1(1) LAPACK auxiliary routine (version 3.2) CLAIC1(1)

NAME

CLAIC1 - applies one step of incremental condition estimation in its simplest version

SYNOPSIS

JOB, J, X, SEST, W, GAMMA, SESTPR, S, C )

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

PURPOSE

CLAIC1 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
twonorm(L*x) = sest
Then CLAIC1 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 system
diag(sest*sest, 0) + [alpha gamma] * [ conjg(alpha) ]
[ conjg(gamma) ] where alpha = conjg(x)'*w.

ARGUMENTS

= 1: an estimate for the largest singular value is computed.
= 2: an estimate for the smallest singular value is computed.
Length of X and W
The j-vector x.
Estimated singular value of j by j matrix L
The j-vector w.
The diagonal element gamma.
Estimated singular value of (j+1) by (j+1) matrix Lhat.
Sine needed in forming xhat.
Cosine needed in forming xhat.
November 2008 LAPACK auxiliary routine (version 3.2)