sptrfs(3)

NAME

SPTRFS - improve the computed solution to a system of lin

ear equations when the coefficient matrix is symmetric positive

definite and tridiagonal, and provides error bounds and backward

error estimates for the solution

SYNOPSIS

SUBROUTINE  SPTRFS( N, NRHS, D, E, DF, EF, B, LDB, X, LDX,
FERR, BERR, WORK, INFO )
    INTEGER        INFO, LDB, LDX, N, NRHS
    REAL           B( LDB, * ), BERR( * ), D( * ),  DF(  *
), E( * ), EF( * ), FERR( * ), WORK( * ), X( LDX, * )

PURPOSE

SPTRFS improves the computed solution to a system of lin

ear equations when the coefficient matrix is symmetric positive

definite and tridiagonal, and provides error bounds and backward

error estimates for the solution.

ARGUMENTS

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 matrix B. NRHS >= 0.

D (input) REAL array, dimension (N)

The n diagonal elements of the tridiagonal matrix

A.

E (input) REAL array, dimension (N-1)

The (n-1) subdiagonal elements of the tridiagonal

matrix A.

DF (input) REAL array, dimension (N)

The n diagonal elements of the diagonal matrix D

from the factorization computed by SPTTRF.

EF (input) REAL array, dimension (N-1)

The (n-1) subdiagonal elements of the unit bidiag

onal factor L from the factorization computed by SPTTRF.

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

SPTTRS. 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 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 up

per bound for the magnitude of the largest element in (X(j)

XTRUE) divided by the magnitude of the largest element in X(j).

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 solution).

WORK (workspace) REAL array, dimension (2*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

SPTRFS(3)