共查询到20条相似文献,搜索用时 672 毫秒
1.
Liu Liu 《Journal of Mathematical Analysis and Applications》2011,378(1):359-373
It has been treated as a difficult problem to find iterative roots of non-monotonic functions. For some PM functions which do not increase the number of forts under iteration a method was given to obtain a non-monotonic iterative root by extending a monotone iterative root from the characteristic interval. In this paper we prove that every continuous iterative root is an extension from the characteristic interval and give various modes of extension for those iterative roots of PM functions. 相似文献
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For PM functions of height 1, the existence of continuous iterative roots of any order was obtained under the characteristic endpoints condition. A natural open question about iterative roots without that condition was raised. This question was answered partially in the case that the function is increasing on its characteristic interval. In this paper, to the opposite, we consider the decreasing case and give the existence and nonexistence results for their iterative roots. 相似文献
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Based on the iterative root theory for monotone functions, an algorithm for computing polygonal iterative roots of increasing polygonal functions was given by J. Kobza. In this paper we not only give an algorithm for roots of decreasing polygonal functions but also generalize Kobza's results to the general n. Furthermore, we extend our algorithms for polygonal PM functions, a class of non-monotonic functions. 相似文献
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Iterative root problem can be regarded as a weak version of the problem of embedding a homeomorphism into a flow. There are
many results on iterative roots of monotone functions. However, this problem gets more diffcult in non-monotone cases. Therefore,
it is interesting to find iterative roots of linear fractional functions (abbreviated as LFFs), a class of non-monotone functions
on ℝ. In this paper, iterative roots of LFFs are studied on ℂ. An equivalence between the iterative functional equation for
non-constant LFFs and the matrix equation is given. By means of a method of finding matrix roots, general formulae of all
meromorphic iterative roots of LFFs are obtained and the precise number of roots is also determined in various cases. As applications,
we present all meromorphic iterative roots for functions z and 1/z.
This work was supported by the Youth Fund of Sichuan Provincial Education Department of China (Grant No. 07ZB042) 相似文献
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It is known that any continuous piecewise monotonic function with nonmonotonicity height not less than 2 has no continuous iterative roots of order n greater than the number of forts of the function. In this paper, we consider the problem of iterative roots in the case that the order n is less than or equal to the number of forts. By investigating the trajectory of possible continuous roots, we give a general method to find all iterative roots of those functions with finite nonmonotonicity height. 相似文献
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It is known that a strictly piecewise monotone function with nonmonotonicity height ≥ 2 on a compact interval has no iterative roots of order greater than the number of forts. An open question is: Does it have iterative roots of order less than or equal to the number of forts? An answer was given recently in the case of "equal to". Since many theories of resultant and algebraic varieties can be applied to computation of polynomials, a special class of strictly piecewise monotone functions, in this paper we investigate the question in the case of "less than" for polynomials. For this purpose we extend the question from a compact interval to the whole real line and give a procedure of computation for real polynomial iterative roots. Applying the procedure together with the theory of discriminants, we find all real quartic polynomials of non-monotonicity height 2 which have quadratic polynomial iterative roots of order 2 and answer the question. 相似文献
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Marek Cezary Zdun 《Journal of Difference Equations and Applications》2018,24(5):773-783
AbstractA function f is said to be iteratively convex if f possesses convex iterative roots of all orders. We give several constructions of iteratively convex diffeomorphisms and explain the phenomenon that the non-existence of convex iterative roots is a typical property of convex functions. We show also that a slight perturbation of iteratively convex functions causes loss of iterative convexity. However, every convex function can be approximate by iteratively convex functions. 相似文献
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Using the forms of Newton iterative function, the iterative function of Newton's method to handle the problem of multiple roots and the Halley iterative function, we give a class of iterative formulae for solving equations in one variable in this paper and show that their convergence order is at least quadratic. At last we employ our methods to solve some non-linear equations and compare them with Newton's method and Halley's method. Numerical results show that our iteration schemes are convergent if we choose two suitable parametric functions λ(x) and μ(x). Therefore, our iteration schemes are feasible and effective. 相似文献
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《中国科学 数学(英文版)》2017,(8)
The polynomial-like iterative equation is an important form of functional equations, in which iterates of the unknown function are linked in a linear combination. Most of known results were given for the given function to be monotone. We discuss this equation for continuous solutions in the case that the given function is a PM(piecewise monotone) function, a special class of non-monotonic functions. Using extension method, we give a general construction of solutions for the polynomial-like iterative equation. 相似文献
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关于一类具有大范围收敛性的迭代法 总被引:3,自引:0,他引:3
本文由Hadamard因子分解定理出发,证明了推广的Laguerre迭代方法对求解一类超越方程具有大范围收敛性.对复根允许存在的区域作了讨论.得出了Riemann假定成立的一个必要条件.还给出了此迭代法的Algol 60程序. 相似文献
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This paper concentrates on iterative methods for obtaining the multiple roots of nonlinear equations. Using the computer algebra system Mathematica, we construct an iterative scheme and discuss the conditions to obtain fourth-order methods from it. All the presented fourth-order methods require one-function and two-derivative evaluation per iteration, and are optimal higher-order iterative methods for obtaining multiple roots. We present some special methods from the iterative scheme, including some known already. Numerical examples are also given to show their performance. 相似文献
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In this survey paper we present some recent results in the iteration theory. Mainly, we focus on the problems concerning real iteration groups (flows) and semigroups (semiflows) such as existence, regularity and embeddability. We also discuss some issues associated to the problem of embedddability, i.e. iterative roots and approximate iterability. The topics of this paper are: (1) measurable iteration semigroups; (2) embedding of diffeomorphisms in regular iteration semigroups in \({{\mathbb{R}}^n}\) space; (3) iteration groups of fixed point free homeomorphisms on the plane; (4) embedding of interval homeomorphisms with two fixed points in a regular iteration group; (5) commuting functions and embeddability; (6) iterative roots; (7) the structure of iteration groups on an interval; (8) iteration groups of homeomorphisms of the circle; (9) approximately iterable functions; (10) set-valued iteration semigroups; (11) iterations of mean-type mappings; (12) Hayers–Ulam stability of the translation equation. Most of the results presented here was obtained by the means of functional equations. We indicate the relations between the iteration theory and functional equations. 相似文献
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A one-parameter family of iterative methods is presented for finding the roots of transcendental equations. For a class of entire functions this family is shown to converge monotonically and globally. We also establish that for simple roots, when a model parameterh is sufficiently small, the convergence is at a linear rate with orderh
2.This work is supported in part by NSERC Grant No. 079-6016. 相似文献
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Wenmeng Zhang Yingying Zeng Witold Jarczyk Weinian Zhang 《Journal of Mathematical Analysis and Applications》2012,386(1):75-82
Stability of iterative roots is important in the numerical computation of iterative roots. Known results show that under some conditions iterative roots of strictly monotonic self-mappings are stable in both the local sense and the global sense. In this paper we discuss the stability for iterative roots of strictly increasing self-mappings on a compact interval between two fixed points. We prove that those iterative roots are locally stable but globally unstable. 相似文献
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研究了函数方程$f^{[m]}=1/f$,分析了逐段连续解的特点,构造性地得到了所有逐段连续的实解.结果推广了[Amer. Math. Monthly 1998, 105(8): 704-717]上的结果,而且得到了不满足Babbage方程的函数没有实的循环迭代根. 相似文献
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In this paper, we investigate the construction of some two-step without memory iterative classes of methods for finding simple roots of nonlinear scalar equations. The classes are built through the approach of weight functions and these obtained classes reach the optimal order four using one function and two first derivative evaluations per full cycle. This shows that our classes can be considered as Jarratt-type schemes. The accuracy of the classes is tested on a number of numerical examples. And eventually, it is observed that our contributions take less number of iterations than the compared existing methods of the same type to find more accurate approximate solutions of the nonlinear equations. 相似文献