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

CHERFS(l)					)					CHERFS(l)

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

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

	   CHARACTER	  UPLO

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

	   INTEGER	  IPIV( * )

	   REAL 	  BERR( * ), FERR( * ), RWORK( * )

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

PURPOSE
       CHERFS improves the computed solution to a system of linear equations when the coefficient
       matrix is Hermitian 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) COMPLEX 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 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**H or A = L*D*L**H as computed by CHETRF.

       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 CHETRF.

       B       (input) COMPLEX 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 array, dimension (LDX,NRHS)
	       On  entry,  the	solution  matrix X, as computed by CHETRS.  On exit, the improved
	       solution matrix X.

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

       FERR    (output) REAL 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) REAL 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 array, dimension (2*N)

       RWORK   (workspace) REAL 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 				CHERFS(l)


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