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

SPPRFS(l)					)					SPPRFS(l)

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

SYNOPSIS
       SUBROUTINE SPPRFS( UPLO, N, NRHS, AP, AFP, B, LDB, X, LDX, FERR, BERR, WORK, IWORK, INFO )

	   CHARACTER	  UPLO

	   INTEGER	  INFO, LDB, LDX, N, NRHS

	   INTEGER	  IWORK( * )

	   REAL 	  AFP(	*  ),  AP(  * ), B( LDB, * ), BERR( * ), FERR( * ), WORK( * ), X(
			  LDX, * )

PURPOSE
       SPPRFS improves the computed solution to a system of linear equations when the coefficient
       matrix  is  symmetric positive definite and packed, 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.

       AP      (input) REAL array, dimension (N*(N+1)/2)
	       The upper or lower triangle of the symmetric matrix A, packed columnwise in a lin-
	       ear array.  The j-th column of A is stored in the array AP as follows: if  UPLO	=
	       'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; if UPLO = 'L', AP(i + (j-1)*(2n-j)/2)
	       = A(i,j) for j<=i<=n.

       AFP     (input) REAL array, dimension (N*(N+1)/2)
	       The triangular factor U or L from the Cholesky factorization A =  U**T*U  or  A	=
	       L*L**T,	as  computed by SPPTRF/CPPTRF, packed columnwise in a linear array in the
	       same format as A (see AP).

       B       (input) REAL 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) REAL array, dimension (LDX,NRHS)
	       On entry, the solution matrix X, as computed by SPPTRS.	 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) REAL 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 				SPPRFS(l)


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