Complexity in iteration of polynomials
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In order to discuss the complexity of nonmonotonicity of a given PM function, it is needed to determine the height of PM functions. But it is not easy to do even for a polynomial because there are great difficulties in determining the number of real zeros for polynomials of higher degrees. In this paper we introduce two iterative sets to determine the nonmonotonicity height for polynomials and give a numerical algorithm for computing the height of general polynomials.
KeywordsPolynomials Nonmonotonicity height Level set Descendants
Mathematics Subject Classification26A18 39B12 68W30
The authors are very grateful to Professor Weinian Zhang for his several valuable suggestions and corrections in our expression. The authors also sincerely thank the referees for their encouragement and helpful comments and suggestions.
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