subroutine slaic1 (JOB, J, X, SEST, W, GAMMA, SESTPR, S, C)
SLAIC1 applies one step of incremental condition estimation.
SLAIC1 applies one step of incremental condition estimation.
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**T 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]**T and sestpr**2 is an eigenpair of the system
diag(sest*sest, 0) + [alpha gamma] * [ alpha ]
[ gamma ]
where alpha = x**T*w.
Parameters:
JOB is INTEGER
= 1: an estimate for the largest singular value is computed.
= 2: an estimate for the smallest singular value is computed.
J
J is INTEGER
Length of X and W
X
X is REAL array, dimension (J)
The j-vector x.
SEST
SEST is REAL
Estimated singular value of j by j matrix L
W
W is REAL array, dimension (J)
The j-vector w.
GAMMA
GAMMA is REAL
The diagonal element gamma.
SESTPR
SESTPR is REAL
Estimated singular value of (j+1) by (j+1) matrix Lhat.
S
S is REAL
Sine needed in forming xhat.
C
C is REAL
Cosine needed in forming xhat.
Author:
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
Definition at line 136 of file slaic1.f.
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