f04atf

f04atf © Numerical Algorithms Group, 2002.

Purpose

F04ATF Accurate solution of real simultaneous linear equations, one right-hand side (Black Box)

Synopsis

[c,ifail] = f04atf(a,b<,ifail>)

Description

 
 Given a set of real linear equations, Ax=b, the routine first 
 computes an LU factorization of A with partial pivoting, PA=LU, 
 where P is a permutation matrix, L is lower triangular and U is 
 unit upper triangular. An approximation to x is found by forward 
 and backward substitution in Ly=Pb and Ux=y. The residual vector 
 r=b-Ax is then calculated using additional precision, and a 
 correction d to x is found by solving LUd=r. x is replaced by x+d
 , and this iterative refinement of the solution is repeated until
 full machine accuracy is obtained.

Parameters

f04atf

Required Input Arguments:

a (:,:)                               real
b (:)                                 real

Optional Input Arguments:                       <Default>

ifail                                 integer  -1

Output Arguments:

c (:)                                 real
ifail                                 integer