Figure Properties - SERC

Examples Example 1.
A = gallery('wilk',21);
b = sum(A,2);
tol = 1e-12;
maxit = 15;
M1 = diag([10:-1:1 1 1:10]);
gmres
x = gmres(A,b,10,tol,maxit,M1,[],[]);
gmres(10) converged at iteration 2(10) to a solution with relative
residual 1.9e-013
Alternatively, use this matrix-vector product function
function y = afun(x,n)
y = [0;
x(1:n-1)] + [((n-1)/2:-1:0)';
(1:(n-1)/2)'] .*x + [x(2:n);
0];
and this preconditioner backsolve function
function y = mfun(r,n)
y = r ./ [((n-1)/2:-1:1)'; 1; (1:(n-1)/2)'];
as inputs to gmres
x1 = gmres(@afun,b,10,tol,maxit,@mfun,[],[],21);
Note that both afun and mfun must accept the gmres extra input n=21.
Example 2.
load west0479
A = west0479
b = sum(A,2)
[x,flag] = gmres(A,b,5)
flag is 1 because gmres does not converge to the default tolerance 1e-6 within
the default 10 outer iterations.
[L1,U1] = luinc(A,1e-5);
[x1,flag1] = gmres(A,b,5,1e-6,5,L1,U1);
2-983