DPTRFS - 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 DPTRFS( N, NRHS, D, E, DF, EF, B, LDB, X, LDX,
FERR, BERR, WORK, INFO )
INTEGER INFO, LDB, LDX, N, NRHS
DOUBLE PRECISION B( LDB, * ), BERR( * ), D( *
), DF( * ), E( * ), EF( * ), FERR( * ),
WORK( * ), X( LDX, * )
PURPOSE
DPTRFS 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) DOUBLE PRECISION array, dimension (N)
The n diagonal elements of the tridiagonal matrix
A.
E (input) DOUBLE PRECISION array, dimension (N-1)
The (n-1) subdiagonal elements of the tridiagonal
matrix A.
DF (input) DOUBLE PRECISION array, dimension (N)
The n diagonal elements of the diagonal matrix D
from the factorization computed by DPTTRF.
EF (input) DOUBLE PRECISION array, dimension (N-1)
The (n-1) subdiagonal elements of the unit bidiag
onal factor L from the factorization computed by
DPTTRF.
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).
dimension (LDX,NRHS)
On entry, the solution matrix X, as computed by
DPTTRS. 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 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).
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
(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.
Man(1) output converted with
man2html