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

DSYRFS(l)					)					DSYRFS(l)

NAME
       DSYRFS  -  improve  the computed solution to a system of linear equations when the coeffi-
       cient matrix is symmetric indefinite, and provides error bounds and backward  error  esti-
       mates for the solution

SYNOPSIS
       SUBROUTINE DSYRFS( UPLO,  N,  NRHS,  A,	LDA,  AF, LDAF, IPIV, B, LDB, X, LDX, FERR, BERR,
			  WORK, IWORK, INFO )

	   CHARACTER	  UPLO

	   INTEGER	  INFO, LDA, LDAF, LDB, LDX, N, NRHS

	   INTEGER	  IPIV( * ), IWORK( * )

	   DOUBLE	  PRECISION A( LDA, * ), AF( LDAF, * ), B( LDB, * ), BERR( * ),  FERR(	*
			  ), WORK( * ), X( LDX, * )

PURPOSE
       DSYRFS improves the computed solution to a system of linear equations when the coefficient
       matrix is symmetric indefinite, and provides error bounds and backward error estimates for
       the solution.

ARGUMENTS
       UPLO    (input) CHARACTER*1
	       = 'U':  Upper triangle of A is stored;
	       = 'L':  Lower triangle of A is stored.

       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 matrices B and
	       X.  NRHS >= 0.

       A       (input) DOUBLE PRECISION array, dimension (LDA,N)
	       The symmetric matrix A.	If UPLO = 'U', the leading N-by-N upper  triangular  part
	       of  A  contains	the upper triangular part of the matrix A, and the strictly lower
	       triangular part of A is not referenced.	If UPLO = 'L', the leading  N-by-N  lower
	       triangular  part  of A contains the lower triangular part of the matrix A, and the
	       strictly upper triangular part of A is not referenced.

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

       AF      (input) DOUBLE PRECISION array, dimension (LDAF,N)
	       The factored form of the matrix A.  AF contains the block diagonal  matrix  D  and
	       the  multipliers  used  to  obtain  the	factor	U or L from the factorization A =
	       U*D*U**T or A = L*D*L**T as computed by DSYTRF.

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

       IPIV    (input) INTEGER array, dimension (N)
	       Details of the interchanges and the block structure of D as determined by DSYTRF.

       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 DSYTRS.	 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  estimated  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).	The esti-
	       mate is as reliable as the estimate for RCOND, and is almost always a slight over-
	       estimate of the true error.

       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 (3*N)

       IWORK   (workspace) INTEGER array, dimension (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 				DSYRFS(l)


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