MATLAB Function Reference Volume 1: A - E - Bad Request

icgstab
2-156
M1 = diag([10:-1:1 1 1:10]);
x = bicgstab(A,b,tol,maxit,M1,[],[]);
bicgstab converged at iteration 12.5 to a solution with relative
residual 1.2e-014
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 bicgstab
x1 = bicgstab(@afun,b,tol,maxit,@mfun,[],[],21);
Note that both afun and mfun must accept bicgstab's extra input n=21.
Example 2.
load west0479;
A = west0479;
b = sum(A,2);
[x,flag] = bicgstab(A,b)
flag is 1 because bicgstab does not converge to the default tolerance 1e-6
within the default 20 iterations.
[L1,U1] = luinc(A,1e-5);
[x1,flag1] = bicgstab(A,b,1e-6,20,L1,U1)
flag1 is 2 because the upper triangular U1 has a zero on its diagonal. This
causes bicgstab to fail in the first iteration when it tries to solve a system such
as U1*y = r using backslash.
[L2,U2] = luinc(A,1e-6);
[x2,flag2,relres2,iter2,resvec2] = bicgstab(A,b,1e-15,10,L2,U2)