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Livre :
Expressions régulières,
Syntaxe et mise en oeuvre :

ISBN : 978-2-7460-9712-4
EAN : 9782746097124
(Editions ENI)

GNU/Linux	CentOS 4.8	i386
	slaic1(l)

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SLAIC1

NAME
SYNOPSIS
PURPOSE
ARGUMENTS

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NAME

SLAIC1 - applie one step of incremental condition estimation 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 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 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 system

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.

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slaic1(l)