f04maf
f04maf
© Numerical Algorithms Group, 2002.
Purpose
F04MAF Real sparse symmetric positive-definite simultaneous linear
equations (coefficient matrix already factorized)
Synopsis
[b,work,acc,noits,ifail] = f04maf(nz,a,irn,icn,b,wkeep,ikeep,inform<,acc,...
noits,ifail>)
Description
F04MAF solves the n linear equations
Ax=b, (1)
where A is a sparse symmetric positive-definite matrix, following
the incomplete Cholesky factorization by F01MAF, given by
T T
C=PLDL P , WAW=C+E,
where P is a permutation matrix, L is a unit lower triangular
matrix, D is a diagonal matrix with positive diagonal elements, E
is an error matrix representing elements dropped during the
factorization and diagonal elements that have been modified to
ensure that C is positive-definite, and W is a diagonal matrix,
chosen to make the diagonal elements of WAW unity.
Equation (1) is solved by applying a pre-conditioned conjugate
gradient method to the equations
-1
(WAW)(W x)=Wb, (2)
using C as the pre-conditioning matrix.
The iterative procedure is terminated if
||Wr|| <=(eta), (3)
2
where r is the residual vector r=b-Ax, ||r|| denotes the
2
Euclidean length of r, (eta) is a user-supplied tolerance and x
is the current approximation to the solution. Notice that
-1
Wr=Wb-(WAW)(W x)
so that Wr is the residual of the normalised equations (2).
Parameters
f04maf
Required Input Arguments:
nz integer
a (:) real
irn (:) integer
icn (:) integer
b (:) real
wkeep (:,3) real
ikeep (:,2) integer
inform (4) integer
Optional Input Arguments: <Default>
acc (2) real [eps;0]
noits (2) integer [100;0]
ifail integer -1
Output Arguments:
b (:) real
work (:) real
acc (2) real
noits (2) integer
ifail integer