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

ZPORFS(l)					)					ZPORFS(l)

NAME
       ZPORFS  -  improve  the computed solution to a system of linear equations when the coeffi-
       cient matrix is Hermitian positive definite,

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

	   CHARACTER	  UPLO

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

	   DOUBLE	  PRECISION BERR( * ), FERR( * ), RWORK( * )

	   COMPLEX*16	  A( LDA, * ), AF( LDAF, * ), B( LDB, * ), WORK( * ), X( LDX, * )

PURPOSE
       ZPORFS improves the computed solution to a system of linear equations when the coefficient
       matrix is Hermitian positive definite, and provides error bounds and backward error  esti-
       mates 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) COMPLEX*16 array, dimension (LDA,N)
	       The Hermitian 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) COMPLEX*16 array, dimension (LDAF,N)
	       The triangular factor U or L from the Cholesky factorization A =  U**H*U  or  A	=
	       L*L**H, as computed by ZPOTRF.

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

       B       (input) COMPLEX*16 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) COMPLEX*16 array, dimension (LDX,NRHS)
	       On  entry,  the	solution  matrix X, as computed by ZPOTRS.  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) COMPLEX*16 array, dimension (2*N)

       RWORK   (workspace) DOUBLE PRECISION 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 				ZPORFS(l)


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