Research On The Iteration Algorithm For Solving System Of Nonlinear Equations

In many applications of engineering,it is inevitable to contact the solution of nonlinear equations or system of nonlinear equations,so it is still a very traditional but important research direction to to solve nonlinear equations efficiently and rapidly.In recent years,it is an efficient research direction that many scholars take the way of improving the classical methods,such as Newton's iteration methods and Chebyshev's methods to search some new iteration algorithms with faster speed of convergence.Based on the investigation of the research background and status of higher order convergence algorithms for solving nonlinear equations,I summarized several classical algorithms and some improved algorithms based on classical algorithms in this paper.As for study of solving nonlinear equation,a family of iterative algorithms is proposed by contacting the Newton's iteration method and the Chebyshev's algorithm,and the convergence analysis shows that the algorithm is of convergence order with 2p+2.The efficiency indexes,which are computed from three special example algorithms with convergence order of 12,16,18 respectively,represent the family of iterative algorithms and show that the family of algorithms has higher efficiency.For the research of solving the system of nonlinear equations,two kinds of iterative algorithm with convergence order 5 are found with inspiration of Newton's iteration method,Runge-Kutta's method and the King algorithm for solving nonlinear equation.The experiences and comparison of the two kinds of algorithm's efficiency indexes with other iterative algorithms' show that the proposed method for solving nonlinear equations is faster and more efficient.