Developer Reference

  • 2020.2
  • 07/15/2020
  • Public Content
Contents

?gbcon

Estimates the reciprocal of the condition number of a band matrix in the 1-norm or the infinity-norm.

Syntax

call sgbcon
(
norm
,
n
,
kl
,
ku
,
ab
,
ldab
,
ipiv
,
anorm
,
rcond
,
work
,
iwork
,
info
)
call dgbcon
(
norm
,
n
,
kl
,
ku
,
ab
,
ldab
,
ipiv
,
anorm
,
rcond
,
work
,
iwork
,
info
)
call cgbcon
(
norm
,
n
,
kl
,
ku
,
ab
,
ldab
,
ipiv
,
anorm
,
rcond
,
work
,
rwork
,
info
)
call zgbcon
(
norm
,
n
,
kl
,
ku
,
ab
,
ldab
,
ipiv
,
anorm
,
rcond
,
work
,
rwork
,
info
)
call gbcon
(
ab
,
ipiv
,
anorm
,
rcond
[
,
kl
]
[
,
norm
]
[
,
info
]
)
Include Files
  • mkl.fi
    ,
    lapack.f90
Description
The routine estimates the reciprocal of the condition number of a general band matrix
A
in the 1-norm or infinity-norm:
κ
1
(
A
) = ||
A
||
1
||
A
-1
||
1
=
κ
(
A
T
) =
κ
(
A
H
)
κ
(
A
) = ||
A
||
||
A
-1
||
=
κ
1
(
A
T
) =
κ
1
(
A
H
).
An estimate is obtained for
||
A
-1
||
, and the reciprocal of the condition number is computed as
rcond
= 1 / (||
A
|| ||
A
-1
||)
.
Before calling this routine:
  • compute
    anorm
    (either ||
    A
    ||
    1
    = max
    j
    Σ