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

DPBRFS(l)					)					DPBRFS(l)

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

SYNOPSIS
       SUBROUTINE DPBRFS( UPLO,  N,  KD,  NRHS, AB, LDAB, AFB, LDAFB, B, LDB, X, LDX, FERR, BERR,
			  WORK, IWORK, INFO )

	   CHARACTER	  UPLO

	   INTEGER	  INFO, KD, LDAB, LDAFB, LDB, LDX, N, NRHS

	   INTEGER	  IWORK( * )

	   DOUBLE	  PRECISION AB( LDAB, * ), AFB( LDAFB, * ), B( LDB, * ), BERR( * ), FERR(
			  * ), WORK( * ), X( LDX, * )

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

       KD      (input) INTEGER
	       The  number of superdiagonals of the matrix A if UPLO = 'U', or the number of sub-
	       diagonals if UPLO = 'L'.  KD >= 0.

       NRHS    (input) INTEGER
	       The number of right hand sides, i.e., the number of columns of the matrices B  and
	       X.  NRHS >= 0.

       AB      (input) DOUBLE PRECISION array, dimension (LDAB,N)
	       The  upper  or  lower triangle of the symmetric band matrix A, stored in the first
	       KD+1 rows of the array.	The j-th column of A is stored in the j-th column of  the
	       array AB as follows: if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
	       if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+kd).

       LDAB    (input) INTEGER
	       The leading dimension of the array AB.  LDAB >= KD+1.

       AFB     (input) DOUBLE PRECISION array, dimension (LDAFB,N)
	       The triangular factor U or L from the Cholesky factorization A =  U**T*U  or  A	=
	       L*L**T of the band matrix A as computed by DPBTRF, in the same storage format as A
	       (see AB).

       LDAFB   (input) INTEGER
	       The leading dimension of the array AFB.	LDAFB >= KD+1.

       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 DPBTRS.	 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 				DPBRFS(l)


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