Provided by: liblapack-doc_3.3.1-1_all NAME

LAPACK-3 - applies one step of incremental condition estimation in its simplest version

SYNOPSIS

SUBROUTINE DLAIC1( JOB, J, X, SEST, W, GAMMA, SESTPR, S, C )

INTEGER        J, JOB

DOUBLE         PRECISION C, GAMMA, S, SEST, SESTPR

DOUBLE         PRECISION W( J ), X( J )

PURPOSE

DLAIC1 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 DLAIC1 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.

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) DOUBLE PRECISION array, dimension (J)
The j-vector x.

SEST    (input) DOUBLE PRECISION
Estimated singular value of j by j matrix L

W       (input) DOUBLE PRECISION array, dimension (J)
The j-vector w.

GAMMA   (input) DOUBLE PRECISION
The diagonal element gamma.

SESTPR  (output) DOUBLE PRECISION
Estimated singular value of (j+1) by (j+1) matrix Lhat.

S       (output) DOUBLE PRECISION
Sine needed in forming xhat.

C       (output) DOUBLE PRECISION
Cosine needed in forming xhat.

LAPACK auxiliary routine (version 3.3.1)   April 2011                            DLAIC1(3lapack)