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RedHat 9 (Linux i386) - man page for dptrfs (redhat section l)

DPTRFS(l)					)					DPTRFS(l)

NAME
       DPTRFS  -  improve  the computed solution to a system of linear equations when the coeffi-
       cient matrix is symmetric positive definite and tridiagonal, and provides error bounds and
       backward error estimates for the solution

SYNOPSIS
       SUBROUTINE DPTRFS( N, NRHS, D, E, DF, EF, B, LDB, X, LDX, FERR, BERR, WORK, INFO )

	   INTEGER	  INFO, LDB, LDX, N, NRHS

	   DOUBLE	  PRECISION  B(  LDB,  *  ), BERR( * ), D( * ), DF( * ), E( * ), EF( * ),
			  FERR( * ), WORK( * ), X( LDX, * )

PURPOSE
       DPTRFS improves the computed solution to a system of linear equations when the coefficient
       matrix is symmetric positive definite and tridiagonal, and provides error bounds and back-
       ward error estimates for the solution.

ARGUMENTS
       N       (input) INTEGER
	       The order of the matrix A.  N >= 0.

       NRHS    (input) INTEGER
	       The number of right hand sides, i.e., the number of columns of the matrix B.  NRHS
	       >= 0.

       D       (input) DOUBLE PRECISION array, dimension (N)
	       The n diagonal elements of the tridiagonal matrix A.

       E       (input) DOUBLE PRECISION array, dimension (N-1)
	       The (n-1) subdiagonal elements of the tridiagonal matrix A.

       DF      (input) DOUBLE PRECISION array, dimension (N)
	       The  n  diagonal elements of the diagonal matrix D from the factorization computed
	       by DPTTRF.

       EF      (input) DOUBLE PRECISION array, dimension (N-1)
	       The (n-1) subdiagonal elements of the unit bidiagonal factor L from the factoriza-
	       tion computed by DPTTRF.

       B       (input) DOUBLE PRECISION array, dimension (LDB,NRHS)
	       The right hand side matrix B.

       LDB     (input) INTEGER
	       The leading dimension of the array B.  LDB >= max(1,N).

       X       (input/output) DOUBLE PRECISION array, dimension (LDX,NRHS)
	       On  entry,  the	solution  matrix X, as computed by DPTTRS.  On exit, the improved
	       solution matrix X.

       LDX     (input) INTEGER
	       The leading dimension of the array X.  LDX >= max(1,N).

       FERR    (output) DOUBLE PRECISION array, dimension (NRHS)
	       The forward error bound for each solution vector X(j)  (the  j-th  column  of  the
	       solution  matrix X).  If XTRUE is the true solution corresponding to X(j), FERR(j)
	       is an estimated upper bound for the magnitude of the largest element  in  (X(j)	-
	       XTRUE) divided by the magnitude of the largest element in X(j).

       BERR    (output) DOUBLE PRECISION array, dimension (NRHS)
	       The  componentwise relative backward error of each solution vector X(j) (i.e., the
	       smallest relative change in any element of A or B that makes X(j) an  exact  solu-
	       tion).

       WORK    (workspace) DOUBLE PRECISION array, dimension (2*N)

       INFO    (output) INTEGER
	       = 0:  successful exit
	       < 0:  if INFO = -i, the i-th argument had an illegal value

PARAMETERS
       ITMAX is the maximum number of steps of iterative refinement.

LAPACK version 3.0			   15 June 2000 				DPTRFS(l)


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