Iterative Roots Of Piecewise Linear Unimodal Functions

In recent years, along with the progress of science and engineering, theory of iteration and iterative roots is also developed continually. Iteration is not only an universal phenomenon in nature and human life, but also a subject on dynamic systems. Its results on chaos bring again a tremendous impact to the whole knowledge system of human beings, after principle of relativity and quantum mechanics. Iterative equations are those equations which involve iteration as a basic operation and closely link with dynamical systems, differential equations, difference equations and integral equations, have greatly affected science and engineering. The problem of iteration and iterative roots is one of the most basic problems in this theory. In the introduction, the basic theory, the basic result and the basic problem in iteration and iterative roots are introduced briefly.In Chapter 2, some progress in iterative roots of non-monotone functions are introduced, including iterative roots of piecewise monotone functions, k-order iterative roots of k-piece monotone continuous self-mappings on the interval, as well as iterative roots of piecewise expanding self-mappings. In addition, the chapter introduces results on iterative roots of the special functions, such as the polynomials, the piecewise linear functions and the set-valued functions.In Chapter 3, we produce the algorithm to calculate high-order iterative roots of monotone piecewise linear functions. Our algorithm bases on commonly used " successively defining method ", and we overcome the difficulties of inverse function calculation. The algorithm not only provides the possibility for the approximate calculation of iterative roots of general continuous functions,...