dptcon (l)  Linux Man Pages
dptcon: computes the reciprocal of the condition number (in the 1norm) of a real symmetric positive definite tridiagonal matrix using the factorization A = L*D*L**T or A = U**T*D*U computed by DPTTRF
NAME
DPTCON  computes the reciprocal of the condition number (in the 1norm) of a real symmetric positive definite tridiagonal matrix using the factorization A = L*D*L**T or A = U**T*D*U computed by DPTTRFSYNOPSIS
 SUBROUTINE DPTCON(
 N, D, E, ANORM, RCOND, WORK, INFO )
 INTEGER INFO, N
 DOUBLE PRECISION ANORM, RCOND
 DOUBLE PRECISION D( * ), E( * ), WORK( * )
PURPOSE
DPTCON computes the reciprocal of the condition number (in the 1norm) of a real symmetric positive definite tridiagonal matrix using the factorization A = L*D*L**T or A = U**T*D*U computed by DPTTRF. Norm(inv(A)) is computed by a direct method, and the reciprocal of the condition number is computed asARGUMENTS
 N (input) INTEGER
 The order of the matrix A. N >= 0.
 D (input) DOUBLE PRECISION array, dimension (N)
 The n diagonal elements of the diagonal matrix D from the factorization of A, as computed by DPTTRF.
 E (input) DOUBLE PRECISION array, dimension (N1)
 The (n1) offdiagonal elements of the unit bidiagonal factor U or L from the factorization of A, as computed by DPTTRF.
 ANORM (input) DOUBLE PRECISION
 The 1norm of the original matrix A.
 RCOND (output) DOUBLE PRECISION
 The reciprocal of the condition number of the matrix A, computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is the 1norm of inv(A) computed in this routine.
 WORK (workspace) DOUBLE PRECISION array, dimension (N)
 INFO (output) INTEGER

= 0: successful exit
< 0: if INFO = i, the ith 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.