% hilbertproblems.m
format compact
for n = 2:8
    n
    H = hilb(n)
    condition_est = cond(H)

    x = ones(n,1)/3;
    b = H*x;

    % now try to recover x
    xc = H\b 

    % see how bad answer is

    residual = H*xc - b
    rel_residual_norm = norm(residual,inf)/norm(b,inf)

    error = xc - x
    rel_error_norm = norm(error,inf)/norm(x,inf)
end