Two-level Iterative Methods For Solving Systems Of Time-varying Nonlinear Equations

Time-varying problems have received widespread attention in the fields of science and engineering,such as signal processing,robot control,face recognition,online computing,etc.In this paper,we mainly discuss the two-level iterative methods for solving systems of time-varying nonlinear equations.Firstly,the problem of the accuracy for solving systems of time-varying nonlinear equations is concerned.With the help of the classical Newton method,a time-varying Newton method suitable for systems of time-varying nonlinear equations is derived.By introducing the idea of two-level iteration,the classical Newton method is used as an inner iteration to control the accuracy for solving systems of time-varying nonlinear equations,and a two-level Newton iterative method is constructed.Theoretical analysis shows that the method can converge,and the error estimation relating to the selected time interval is given.Secondly,we notice that the derivatives of some time-varying nonlinear equations are not easy to obtain.In order to avoid to evaluate derivatives and with the help of the idea of classical Broyden method,the former method is improved to the two-level inverse Broyden method.Finally,we summarize the general framework of two-level iterative methods,and give the modified two-level Newton method as an example which illustrates that a new two-level iterative method can be constructed by selecting different inner and outer iterative methods under the two-level iterative framework.Numerical experiments show that these methods are all feasible and effective.This paper is mainly divided into five chapters.Chapter 1 mainly introduces the background of ZNN and the two-level iterative methods.Chapter 2 is the preliminary knowledge,mainly reviewing some classic algorithms for systems of nonlinear equations.The two-level Newton iterative method for solving systems of time-varying nonlinear equations,and its convergence and error analysis are given in Chapter 3.The two-level inverse Broyden iterative method is proposed in Chapter 4.Chapter 5 summarizes the general two-level iterative framework,and proposes the modified two-level Newton iterative method.For each iterative method,we verify its effectiveness with numerical experiments.