f04asf

f04asf © Numerical Algorithms Group, 2002.

Purpose

F04ASF Accurate solution of real symmetric positive-definite simultaneous linear equations, one right-hand side (Black Box)

Synopsis

[a,c,ifail] = f04asf(a,b<,ifail>)

Description

 
 Given a set of real linear equations Ax=b, where A is a symmetric
 positive-definite matrix, the routine first computes a Cholesky 
                           T                                
 factorization of A as A=LL  where L is lower triangular. An 
 approximation to x is found by forward and backward substitution.
 The residual vector r=b-Ax is then calculated using additional 
                                                         T      
 precision and a correction d to x is found by solving LL d=r. x 
 is then replaced by x+d, and this iterative refinement of the 
 solution is repeated until machine accuracy is obtained.
 

Parameters

f04asf

Required Input Arguments:

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

Optional Input Arguments:                       <Default>

ifail                                 integer  -1

Output Arguments:

a (:,:)                               real
c (:)                                 real
ifail                                 integer