if we can extend this fixed point method to (p1(y) - p2(y)x), then x_n converges to p1(y)/p2(y), i.e. we can comp…

if we can extend this fixed point method to (p1(y) - p2(y)x), then x_n converges to p1(y)/p2(y), i.e. we can compute any rational function of spectrum, instead of just fractional powers. And rational functions can fit many functions very we