% script: lec40alt.m
% description: performs some preconditioning experiments with CG
% using the preconditioned CG algorithm
m = 1000
% try n = 5, 10, 50
n =5
x = zeros(m,1);
x(2) = 1;
x(101) = 1;
A = toeplitz(x) + diag(0.5+(1:m).^2);
condA = cond(A)
b = ones(m,1);
x = A\b;
M = diag(diag(A));
condMinvA = cond(M\A)
X = pcg(M,A,b,n);
R = A*X - ones(m,n);
r = zeros(n,1);
s = r;
for ii = 1:n, r(ii) = norm(R(:, ii)); end
figure(1);
plot(r);
grid
title('Residual Errors')
normx = norm(x);
relxerr = norm(X(:,n) - x)/normx
E = (X - repmat(x,1,n))/normx;
for ii = 1:n, r(ii) = norm(E(:, ii)); end
figure(2);
plot(r);
title('Solution Errors')