SPTCON - compute the reciprocal of the condition number
(in the 1-norm) of a real symmetric positive definite
tridiagonal matrix using the factorization A = L*D*L**T or
A = U**T*D*U computed by SPTTRF
SYNOPSIS
SUBROUTINE SPTCON( N, D, E, ANORM, RCOND, WORK, INFO )
INTEGER INFO, N
REAL ANORM, RCOND
REAL D( * ), E( * ), WORK( * )
PURPOSE
SPTCON computes the reciprocal of the condition number (in
the 1-norm) of a real symmetric positive definite tridiag
onal matrix using the factorization A = L*D*L**T or A =
U**T*D*U computed by SPTTRF. Norm(inv(A)) is computed by
a direct method, and the reciprocal of the condition num
ber is computed as
RCOND = 1 / (ANORM * norm(inv(A))).
ARGUMENTS
N (input) INTEGER
The order of the matrix A. N >= 0.
D (input) REAL array, dimension (N)
The n diagonal elements of the diagonal matrix D
from the factorization of A, as computed by SPT
TRF.
E (input) REAL array, dimension (N-1)
The (n-1) off-diagonal elements of the unit bidi
agonal factor U or L from the factorization of A,
as computed by SPTTRF.
ANORM (input) REAL
The 1-norm of the original matrix A.
RCOND (output) REAL
The reciprocal of the condition number of the
matrix A, computed as RCOND = 1/(ANORM * AINVNM),
where AINVNM is the 1-norm of inv(A) computed in
this routine.
WORK (workspace) REAL array, dimension (N)
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an ille
gal value
The method used is described in Nicholas J. Higham, "Effi
cient Algorithms for Computing the Condition Number of a
Tridiagonal Matrix", SIAM J. Sci. Stat. Comput., Vol. 7,
No. 1, January 1986.
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