For symmetric indefinite matrices it is best to use the minimum residual algorithm. The following example is slightly modified from the previous example by negating the first matrix element:
/* minimum residual algorithm */
/* value row col */
A = { -3 1 1,
1 2 1,
4 2 2,
1 3 2,
3 4 2,
10 3 3,
3 4 4 };
/* right-hand sides b = (1 1 1 1) */
b = {1, 1, 1, 1};
/* desired solution tolerance (optional) */
tol = 1e-7;
/* maximum number of iterations (optional) */
maxit = 200;
/* allocate iteration progress (optional) */
hist = j(50, 1);
/* initial guess (optional) */
start = {2, 3, 4, 5};
/* invoke minimum residual method */
call itsolver (
x, st, it, /* output parameters */
'minres', a, b, 'ic', /* input parameters */
tol, /* optional control parameters */
maxit,
start,
hist
);
print x; /* print solution */
print st; /* print solution tolerance */
print it; /* print resultant number of iterations */
X
-0.27027
0.1891892
0.0810811
0.1441441
ST
1.283E-15
IT
4