共查询到20条相似文献,搜索用时 15 毫秒
1.
In this paper, we present a new fourth-order method for finding multiple roots of nonlinear equations. It requires one evaluation of the function and two of its first derivative per iteration. Finally, some numerical examples are given to show the performance of the presented method compared with some known third-order methods. 相似文献
2.
In this paper we study iterative roots of PM functions, a special class of non-monotone functions. Problem 2 in [W. Zhang, PM functions, their characteristic intervals and iterative roots, Ann. Polon. Math. LXV (1997) 119-128] is solved partly and Theorem 4 in that paper is generalized. 相似文献
3.
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
4.
In this paper, we consider an iterative method for evaluating the coefficients of a monic factor of an analytic function using complex circular arithmetic. In a previous paper, the authors presented a factoring method that finds a cluster of zeros as a polynomial factor. We analyze the convergence behavior of this method and discuss a technique for improving convergence. Numerical examples illustrate the aspects of the improved method. 相似文献
5.
T. Powierża 《Aequationes Mathematicae》2002,63(1-2):103-109
6.
7.
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
8.
Arc-analytic roots of analytic functions are Lipschitz 总被引:2,自引:0,他引:2
Krzysztof Kurdyka Laurentiu Paunescu 《Proceedings of the American Mathematical Society》2004,132(6):1693-1702
Let be an arc-analytic function (i.e., analytic on every analytic arc) and assume that for some integer the function is real analytic. We prove that is locally Lipschitz; even if is less than the multiplicity of . We show that the result fails if is only a , arc-analytic function (even blow-analytic), . We also give an example of a non-Lipschitz arc-analytic solution of a polynomial equation , where are real analytic functions.
9.
Ioannis K. Argyros Saïd Hilout 《Nonlinear Analysis: Theory, Methods & Applications》2010,72(9-10):3857-3864
We present new results for the local convergence of the Newton-like method to a unique solution of nondifferentiable variational inclusions in a Banach space setting using the Lipschitz-like property of set-valued mappings and the concept of slant differentiability hypothesis on the operator involved, as was introduced by X. Chen, Z. Nashed and L. Qi. The linear convergence of the Newton-like method is also established. Our results extend the applicability of the Newton-like method (Argyros and Hilout, 2009 [5] and Chen, Nashed and Qi, 2000 [7]) to variational inclusions. 相似文献
10.
11.
Tanabe (1988) proposed a variation of the classical Newton method for solving nonlinear systems of equations, the so-called Centered Newton
method. His idea was based on a deviation of the Newton direction towards a variety called “Central Variety”. In this paper
we prove that the Centered Newton method is locally convergent and we present a globally convergent method based on the centered
direction used by Tanabe. We show the effectiveness of our proposal for solving nonlinear system of equations and compare
with the Newton method with line search. 相似文献
12.
For an equation f(x)=0 having a multiple root of multiplicity m>1 unknown, we propose a transformation which converts the multiple root to a simple root of H(x)=0. The transformed function H(x) of f(x) with a small >0 has appropriate properties in applying a derivative free iterative method to find the root. Moreover, there is no need to choose a proper initial approximation. We show that the proposed method is superior to the existing methods by several numerical examples. 相似文献
13.
A successive relaxation iterative algorithm for discrete HJB equations is proposed. Monotone convergence has been proved for
the algorithm.
This work was supported by NNSF of China (no. 10571046). 相似文献
14.
Xiao-Ming Niu Tetsuya Sakurai Hiroshi Sugiura 《Journal of Computational and Applied Mathematics》2007
In this paper, we propose a verified method for bounding clusters of zeros of analytic functions. Our method gives a disk that contains a cluster of m zeros of an analytic function f(z). Complex circular arithmetic is used to perform a validated computation of n -degree Taylor polynomial p(z) of f(z). Some well known formulae for bounding zeros of a polynomial are used to compute a disk containing a cluster of zeros of p(z). A validated computation of an upper bound for Taylor remainder series of f(z) and a lower bound of p(z) on a circle are performed. Based on these results, Rouché's theorem is used to verify that the disk contains the cluster of zeros of f(z). This method is efficient in computation of the initial disk of a method for finding validated polynomial factor of an analytic function. Numerical examples are presented to illustrate the efficiency of the proposed method. 相似文献
15.
V. Antony Vijesh P.V. Subrahmanyam 《Journal of Mathematical Analysis and Applications》2008,339(2):1231-1242
In this paper we prove an existence and uniqueness theorem for solving the operator equation F(x)+G(x)=0, where F is a Gateaux differentiable continuous operator while the operator G satisfies a Lipschitz-condition on an open convex subset of a Banach space. As corollaries, a theorem of Tapia on a weak Newton's method and the classical convergence theorem for modified Newton-iterates are deduced. An existence theorem for a generalized Euler-Lagrange equation in the setting of Sobolev space is obtained as a consequence of the main theorem. We also obtain a class of Gateaux differentiable operators which are nowhere Frechet differentiable. Illustrative examples are also provided. 相似文献
16.
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
17.
It was proved that all continuous functions are topologically conjugate to their continuous iterative roots in monotonic cases. An interesting problem reads: Does the same conclusion hold in non-monotonic cases?We give a negative answer to the problem by presenting a necessary condition for the topological conjugacy,which helps us construct counter examples. We also give a sufficient condition as well as a method of constructing the topological conjugacy. 相似文献
18.
A fast and simple iterative method with cubic convergent is proposed for the determination of the real and complex roots of any function F(x) = 0. The idea is based upon passing a defined function G(x) tangent to F(x) at an arbitrary starting point. Choosing G(x) in the form of xk or kx, where k is obtained for the best correlation with the function F(x), gives an added freedom, which in contrast to all existing methods, accelerates the convergence. Also, this new method can find complex roots just by a real initial guess. This is in contrast to many other methods like the famous Newton method that needs complex initial guesses for finding complex roots. The proposed method is compared to some new and famous methods like Newton method and a modern solver that is fsolve command in MATLAB. The results show the effectiveness and robustness of this new method as compared to other methods. 相似文献
19.
This paper presents a fifth-order iterative method as a new modification of Newton’s method for finding multiple roots of
nonlinear equations with unknown multiplicity m. Its convergence order is analyzed and proved. Moreover, several numerical examples demonstrate that the proposed iterative
method is superior to the existing methods. 相似文献
20.
A new iterative method is proposed for computing partial derivatives of many eigenpairs. This method simultaneously computes a few eigenpair partial derivatives. For each origin shift, partial derivatives of eigenpairs whose eigenvalues are closest to the origin shift can be computed. Hence, this method may be used for partial derivatives of all eigenpairs. Convergence of the proposed method is established. Finally numerical experiments are given to show the effectiveness of the proposed method. 相似文献