dpbrfs(3)

NAME

DPBRFS - improve the computed solution to a system of lin

ear equations when the coefficient 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 lin

ear 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 subdiagonals 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 fol

lows: 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 solu

tion 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 estimate is as reliable as the estimate for RCOND, and

is almost always a slight overestimate 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 solution).

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 ille

gal value

PARAMETERS

ITMAX is the maximum number of steps of iterative refine

ment.

LAPACK version 3.0 15 June 2000

DPBRFS(3)