A modified formula of ancient Chinese algorithm by the homotopy continuation technique

A modified formula, iteration representation, of ancient Chinese algorithm by combining the homotopy continuation technique is presented. Considering the convergence, the new iteration formula and the technique for the choice of the auxiliary homotopy function are developed. Once we have the condition f(x1) = f(x2) or f(x) is an even function, we will diverge in traditional ancient Chinese algorithm. The paper provides some useful rules to overcome this defect.