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

DGBRFS(l)					)					DGBRFS(l)

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

SYNOPSIS
       SUBROUTINE DGBRFS( TRANS,  N,  KL,  KU,	NRHS, AB, LDAB, AFB, LDAFB, IPIV, B, LDB, X, LDX,
			  FERR, BERR, WORK, IWORK, INFO )

	   CHARACTER	  TRANS

	   INTEGER	  INFO, KL, KU, LDAB, LDAFB, LDB, LDX, N, NRHS

	   INTEGER	  IPIV( * ), IWORK( * )

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

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

ARGUMENTS
       TRANS   (input) CHARACTER*1
	       Specifies the form of the system of equations:
	       = 'N':  A * X = B     (No transpose)
	       = 'T':  A**T * X = B  (Transpose)
	       = 'C':  A**H * X = B  (Conjugate transpose = Transpose)

       N       (input) INTEGER
	       The order of the matrix A.  N >= 0.

       KL      (input) INTEGER
	       The number of subdiagonals within the band of A.  KL >= 0.

       KU      (input) INTEGER
	       The number of superdiagonals within the band of A.  KU >= 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  original band matrix A, stored in rows 1 to KL+KU+1.  The j-th column of A is
	       stored in the j-th column of the array AB as follows: AB(ku+1+i-j,j) = A(i,j)  for
	       max(1,j-ku)<=i<=min(n,j+kl).

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

       AFB     (input) DOUBLE PRECISION array, dimension (LDAFB,N)
	       Details of the LU factorization of the band matrix A, as computed by DGBTRF.  U is
	       stored as an upper triangular band matrix with KL+KU superdiagonals in rows  1  to
	       KL+KU+1,  and  the  multipliers	used  during the factorization are stored in rows
	       KL+KU+2 to 2*KL+KU+1.

       LDAFB   (input) INTEGER
	       The leading dimension of the array AFB.	LDAFB >= 2*KL*KU+1.

       IPIV    (input) INTEGER array, dimension (N)
	       The pivot indices from DGBTRF; for 1<=i<=N, row i of the matrix	was  interchanged
	       with row IPIV(i).

       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 DGBTRS.  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 				DGBRFS(l)


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