CLAIC1
Purpose
CLAIC1 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 CLAIC1 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.
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 CLAIC1 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.
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) COMPLEX array, dimension (J)
The j-vector x.
|
| SEST |
(input) REAL
Estimated singular value of j by j matrix L
|
| W |
(input) COMPLEX array, dimension (J)
The j-vector w.
|
| GAMMA |
(input) COMPLEX
The diagonal element gamma.
|
| SESTPR |
(output) REAL
Estimated singular value of (j+1) by (j+1) matrix Lhat.
|
| S |
(output) COMPLEX
Sine needed in forming xhat.
|
| C |
(output) COMPLEX
Cosine needed in forming xhat.
|