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

ZPBRFS(l)					)					ZPBRFS(l)

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

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

	   CHARACTER	  UPLO

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

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

	   COMPLEX*16	  AB( LDAB, * ), AFB( LDAFB, * ), B( LDB, * ), WORK( * ), X( LDX, * )

PURPOSE
       ZPBRFS improves the computed solution to a system of linear equations when the coefficient
       matrix  is  Hermitian 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 Hermitian 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) COMPLEX*16 array, dimension (LDAFB,N)
	       The  triangular	factor	U  or L from the Cholesky factorization A = U**H*U or A =
	       L*L**H of the band matrix A as computed by ZPBTRF, in the same storage format as A
	       (see AB).

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

       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 ZPBTRS.  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 				ZPBRFS(l)


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