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SPTCON(l)) SPTCON(l)NAMESPTCON - compute the reciprocal of the condition number (in the 1-norm) of a real symmet- ric positive definite tridiagonal matrix using the factorization A = L*D*L**T or A = U**T*D*U computed by SPTTRFSYNOPSISSUBROUTINE SPTCON( N, D, E, ANORM, RCOND, WORK, INFO ) INTEGER INFO, N REAL ANORM, RCOND REAL D( * ), E( * ), WORK( * )PURPOSESPTCON 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))).ARGUMENTSN (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 fac- torization 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 =, the i-th argument had an illegal value-iFURTHER DETAILSThe 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.LAPACK version 3.015 June 2000 SPTCON(l)

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