A new iteration method for solving algebraic equations

In this paper, a nonlinear algebraic equation f(x)=0, by applying Taylor's theorem, is converted into a coupled iteration system L(xn+1)+g(xn)=0 and g(xn)=f(xn)−L(xn), where L(x)=Ax2+Bx+C. The formula is of high convergence. Some examples are given.