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 )

void slaic1(long int job, long int j, float ∗sx, float sest,
float ∗w, float gamma, float ∗sestpr, float ∗s, float ∗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.

Sun, Inc.  —  Last change: 20 Sep 1996