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Livre :
Expressions régulières,
Syntaxe et mise en oeuvre :

ISBN : 978-2-7460-9712-4
EAN : 9782746097124
(Editions ENI)

GNU/Linux	CentOS 4.8	i386
	sptcon(l)

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SPTCON

NAME
SYNOPSIS
PURPOSE
ARGUMENTS
FURTHER DETAILS

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NAME

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 tridiagonal 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 number 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 SPTTRF.

E (input) REAL array, dimension (N-1)

The (n-1) off-diagonal elements of the unit bidiagonal 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 illegal value

FURTHER DETAILS

The method used is described in Nicholas J. Higham, "Efficient 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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sptcon(l)