Ch. 8 Numerical calculation method 8-15 S-system solving method superior to Newton-Raphson method

A typical method for finding the roots of nonlinear equations is the Newton-Raphson method. However, this method requires the initial estimates to be close to the roots, otherwise convergence can take a long time or diverge. All root-finding methods have more or less the same problem, and researchers will want to use the method that can avoid this problem the most among them. In this video, hence, I will introduce the S-system solving method, which has a wider convergence range than the Newton-Raphson method and convergence is always quicker within that region. Eq. (15) in page 9 has a mistake. Correct it to f(x)=x^n+x-1. #S-system solving method #Newton-Raphson method #Root-finding method #Mathematical modeling