man slaic1 (Fonctions bibliothèques) - applie one step of incremental condition estimation in its simplest version
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.