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zlaic1.f(3) LAPACK zlaic1.f(3)

zlaic1.f -


subroutine zlaic1 (JOB, J, X, SEST, W, GAMMA, SESTPR, S, C)
 
ZLAIC1 applies one step of incremental condition estimation.

ZLAIC1 applies one step of incremental condition estimation.
Purpose:
 ZLAIC1 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 ZLAIC1 computes sestpr, s, c such that the vector [ s*x ] xhat = [ c ] is an approximate singular vector of [ L 0 ] Lhat = [ w**H 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]**H and sestpr**2 is an eigenpair of the system
diag(sest*sest, 0) + [alpha gamma] * [ conjg(alpha) ] [ conjg(gamma) ]
where alpha = x**H * w.
Parameters:
JOB
          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 COMPLEX*16 array, dimension (J)
          The j-vector x.
SEST
          SEST is DOUBLE PRECISION
          Estimated singular value of j by j matrix L
W
          W is COMPLEX*16 array, dimension (J)
          The j-vector w.
GAMMA
          GAMMA is COMPLEX*16
          The diagonal element gamma.
SESTPR
          SESTPR is DOUBLE PRECISION
          Estimated singular value of (j+1) by (j+1) matrix Lhat.
S
          S is COMPLEX*16
          Sine needed in forming xhat.
C
          C is COMPLEX*16
          Cosine needed in forming xhat.
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
September 2012
Definition at line 136 of file zlaic1.f.

Generated automatically by Doxygen for LAPACK from the source code.
Sat Nov 16 2013 Version 3.4.2

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