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DPTRFS(3F)							    DPTRFS(3F)

NAME
     DPTRFS - improve the computed solution to a system of linear equations
     when the coefficient 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 backward 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 factorization 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).

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DPTRFS(3F)							    DPTRFS(3F)

     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 solution).

     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.

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