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The Equivalence between the Mann and Ishikawa Iterations for Generalized Contraction Mappings in a Cone 被引量:3
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作者 L. Jones Tarcius Doss T. Esakkiappan 《Applied Mathematics》 2011年第11期1369-1371,共3页
In this paper, equivalence between the Mann and Ishikawa iterations for a generalized contraction mapping in cone subset of a real Banach space is discussed.
关键词 mann iteration IsHIKAWA iterations Generalized CONTRACTION CONE
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The Equivalence of Ishikawa-Mann and Multistep Iterations in Banach Space
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作者 Liping Yang 《Numerical Mathematics A Journal of Chinese Universities(English Series)》 SCIE 2007年第1期83-91,共9页
Let E be a real Banach space and T be a continuous Φ-strongly accretive operator. By using a new analytical method, it is proved that the convergence of Mann, Ishikawa and three-step iterations are equivalent to the ... Let E be a real Banach space and T be a continuous Φ-strongly accretive operator. By using a new analytical method, it is proved that the convergence of Mann, Ishikawa and three-step iterations are equivalent to the convergence of multistep iteration. The results of this paper extend the results of Rhoades and Soltuz in some aspects. 展开更多
关键词 巴拿赫空间 泛函分析 叠代 等价性
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MANN AND ISHIKAWA ITERATIVE APPROXIMATION OF SOLUTIONS FOR m-ACCRETIVE OPERATOR EQUATIONS 被引量:1
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作者 张石生 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 1999年第12期1310-1318,共9页
The purpose of this paper is to study the Mann and Ishikawa iterative approximation of solutions for m_accretive operator equations in Banach spaces. The results presented in this paper extend and improve some authors... The purpose of this paper is to study the Mann and Ishikawa iterative approximation of solutions for m_accretive operator equations in Banach spaces. The results presented in this paper extend and improve some authors' recent results. 展开更多
关键词 m _accretive operator mann iterative sequence Ishikawa iterative sequence
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ON THE CONVERGENCE PROBLEMS OF ISHIKAWA AND MANN ITERATIVE PROCESSES WITH ERROR FOR Φ-PSEUDO CONTRACTIVE TYPE MAPPINGS 被引量:1
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作者 张石生 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2000年第1期3-14,共12页
The purpose of this paper is to introduce the concept of Φ_pseudo contractive type mapping and to study the convergence problem of Ishikawa and Mann iterative processes with error for this kind of mappings. The resul... The purpose of this paper is to introduce the concept of Φ_pseudo contractive type mapping and to study the convergence problem of Ishikawa and Mann iterative processes with error for this kind of mappings. The results presented in this paper improve and extend many authors'recent results. 展开更多
关键词 Φ-pseudo contractive type mapping accretive mapping pseudo_contractive mapping Φ_strongly accretive mapping Φ_hemi_contractive mapping Ishikawa iterative processes with error mann iterative process with error
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Design of quantum VQ iteration and quantum VQ encoding algorithm taking O(√N) steps for data compression 被引量:2
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作者 庞朝阳 周正威 +1 位作者 陈平形 郭光灿 《Chinese Physics B》 SCIE EI CAS CSCD 2006年第3期618-623,共6页
Vector quantization (VQ) is an important data compression method. The key of the encoding of VQ is to find the closest vector among N vectors for a feature vector. Many classical linear search algorithms take O(N)... Vector quantization (VQ) is an important data compression method. The key of the encoding of VQ is to find the closest vector among N vectors for a feature vector. Many classical linear search algorithms take O(N) steps of distance computing between two vectors. The quantum VQ iteration and corresponding quantum VQ encoding algorithm that takes O(√N) steps are presented in this paper. The unitary operation of distance computing can be performed on a number of vectors simultaneously because the quantum state exists in a superposition of states. The quantum VQ iteration comprises three oracles, by contrast many quantum algorithms have only one oracle, such as Shor's factorization algorithm and Grover's algorithm. Entanglement state is generated and used, by contrast the state in Grover's algorithm is not an entanglement state. The quantum VQ iteration is a rotation over subspace, by contrast the Grover iteration is a rotation over global space. The quantum VQ iteration extends the Grover iteration to the more complex search that requires more oracles. The method of the quantum VQ iteration is universal. 展开更多
关键词 data compression vector quantization Grover's algorithm quantum VQ iteration
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Parametric Iteration Method for Solving Linear Optimal Control Problems 被引量:1
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作者 Abdolsaeed Alavi Aghileh Heidari 《Applied Mathematics》 2012年第9期1059-1064,共6页
This article presents the Parametric Iteration Method (PIM) for finding optimal control and its corresponding trajectory of linear systems. Without any discretization or transformation, PIM provides a sequence of func... This article presents the Parametric Iteration Method (PIM) for finding optimal control and its corresponding trajectory of linear systems. Without any discretization or transformation, PIM provides a sequence of functions which converges to the exact solution of problem. Our emphasis will be on an auxiliary parameter which directly affects on the rate of convergence. Comparison of PIM and the Variational Iteration Method (VIM) is given to show the preference of PIM over VIM. Numerical results are given for several test examples to demonstrate the applicability and efficiency of the method. 展开更多
关键词 PARAMETRIC iteration METHOD Optimal Control Problem Pontryagin’s Maximum Principle He’s VARIATIONAL iteration METHOD
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Modified two-grid method for solving coupled Navier-Stokes/Darcy model based on Newton iteration 被引量:1
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作者 SHEN Yu-jing HAN Dan-fu SHAO Xin-ping 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2015年第2期127-140,共14页
A new decoupled two-gird algorithm with the Newton iteration is proposed for solving the coupled Navier-Stokes/Darcy model which describes a fluid flow filtrating through porous media. Moreover the error estimate is g... A new decoupled two-gird algorithm with the Newton iteration is proposed for solving the coupled Navier-Stokes/Darcy model which describes a fluid flow filtrating through porous media. Moreover the error estimate is given, which shows that the same order of accuracy can be achieved as solving the system directly in the fine mesh when h = H2. Both theoretical analysis and numerical experiments illustrate the efficiency of the algorithm for solving the coupled problem. 展开更多
关键词 Navier-stokes equation Darcy's law interface coupling two-grid algorithm Newton iteration
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A Monotonicity Condition for Strong Convergence of the Mann Iterative Sequence for Demicontractive Maps in Hilbert Spaces
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作者 Akuchu Besheng George Celestin Akwumbuom Nse 《Applied Mathematics》 2014年第15期2195-2198,共4页
Let?be a real Hilbert space and?C?be a nonempty closed convex subset of H. Let T : C?→?C?be a demicontractive map satisfying?〈Tx, x〉?≥?‖x‖2 for all?x?∈ D (T). Then the Mann iterative sequence given by?xn + 1?= ... Let?be a real Hilbert space and?C?be a nonempty closed convex subset of H. Let T : C?→?C?be a demicontractive map satisfying?〈Tx, x〉?≥?‖x‖2 for all?x?∈ D (T). Then the Mann iterative sequence given by?xn + 1?= (1 - an) xn +?anT xn, where an ∈?(0, 1) n?≥?0, converges strongly to an element of F (T):= {x?∈ C : Tx = x}. This strong convergence is obtained without the compactness-type assumptions on C, which many previous results (see e.g. [1]) employed. 展开更多
关键词 Demicontractive Maps mann iterative sequence strong Convergence MONOTONICITY HILBERT sPACEs
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Convergence Theorems of Mann and Ishikawa Iterative Processes with Errors for Multivalued Φ-strongly Accretive Mapping
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作者 张国伟 《Northeastern Mathematical Journal》 CSCD 2003年第2期174-180,共7页
Let X be a real Banach space and A : X→ 2x a bounded uniformly continuous Φ-strongly accretive multivalued mapping. For any f ∈ X, Mann and Ishikawa iterative processes with errors converge strongly to the unique s... Let X be a real Banach space and A : X→ 2x a bounded uniformly continuous Φ-strongly accretive multivalued mapping. For any f ∈ X, Mann and Ishikawa iterative processes with errors converge strongly to the unique solution of Ax (?) f. The conclusion in this paper weakens the stronger conditions about errors in Chidume and Moore's theorem (J. Math. Anal. Appl, 245(2000), 142-160). 展开更多
关键词 mann and Ishikawa iteration Φ-strongly accretive mapping conver-gence theorem
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A Nonstationary Halley’s Iteration Method by Using Divided Differences Formula
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作者 Nasr Al Din Ide 《Applied Mathematics》 2012年第2期169-171,共3页
This paper presents a new nonstationary iterative method for solving non linear algebraic equations that does not require the use of any derivative. The study uses only the Newton’s divided differences of first and s... This paper presents a new nonstationary iterative method for solving non linear algebraic equations that does not require the use of any derivative. The study uses only the Newton’s divided differences of first and second orders instead of the derivatives of (1). 展开更多
关键词 NONsTATIONARY iterATIVE METHOD Hally’s FORMULA Divided DIFFERENCEs
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Application of He’s Variational Iteration Method for the Analytical Solution of Space Fractional Diffusion Equation
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作者 Mehdi Safari 《Applied Mathematics》 2011年第9期1091-1095,共5页
Spatially fractional order diffusion equations are generalizations of classical diffusion equations which are increasingly used in modeling practical super diffusive problems in fluid flow, finance and others areas of... Spatially fractional order diffusion equations are generalizations of classical diffusion equations which are increasingly used in modeling practical super diffusive problems in fluid flow, finance and others areas of application. This paper presents the analytical solutions of the space fractional diffusion equations by variational iteration method (VIM). By using initial conditions, the explicit solutions of the equations have been presented in the closed form. Two examples, the first one is one-dimensional and the second one is two-dimensional fractional diffusion equation, are presented to show the application of the present techniques. The present method performs extremely well in terms of efficiency and simplicity. 展开更多
关键词 He’s VARIATIONAL iteration Method FRACTIONAL DERIVATIVE FRACTIONAL Diffusion Equation
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On the Deepest Fallacy in the History of Mathematics: The Denial of the Postulate about the Approximation Nature of a Simple-Iteration Method and Iterative Derivation of Cramer’s Formulas
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作者 Albert Iskhakov Sergey Skovpen 《Applied Mathematics》 2019年第6期371-382,共12页
Contrary to the opinion about approximation nature of a simple-iteration method, the exact solution of a system of linear algebraic equations (SLAE) in a finite number of iterations with a stationary matrix is demonst... Contrary to the opinion about approximation nature of a simple-iteration method, the exact solution of a system of linear algebraic equations (SLAE) in a finite number of iterations with a stationary matrix is demonstrated. We present a theorem and its proof that confirms the possibility to obtain the finite process and imposes the requirement for the matrix of SLAE. This matrix must be unipotent, i.e. all its eigenvalues to be equal to 1. An example of transformation of SLAE given analytically to the form with a unipotent matrix is presented. It is shown that splitting the unipotent matrix into identity and nilpotent ones results in Cramer’s analytical formulas in a finite number of iterations. 展开更多
关键词 system of Linear Algebraic Equations (sLAE) NILPOTENT MATRIX Unipotent MATRIX Eigenvalue Assignment Finite iterATIVE Process Cramer’s FORMULAs
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A Comparative Study of Variational Iteration Method and He-Laplace Method
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作者 Hradyesh Kumar Mishra 《Applied Mathematics》 2012年第10期1193-1201,共9页
In this paper, variational iteration method and He-Laplace method are used to solve the nonlinear ordinary and partial differential equations. Laplace transformation with the homotopy perturbation method is called He-... In this paper, variational iteration method and He-Laplace method are used to solve the nonlinear ordinary and partial differential equations. Laplace transformation with the homotopy perturbation method is called He-Laplace method. A comparison is made among variational iteration method and He-Laplace. It is shown that, in He-Laplace method, the nonlinear terms of differential equation can be easily handled by the use of He’s polynomials and provides better results. 展开更多
关键词 Variational iteration METHOD He-Laplace Transform METHOD HOMOTOPY Perturbation METHOD Ordinary DIFFERENTIAL Equation Partial DIFFERENTIAL Equations He’s Polynomials
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Numerical Solution of Generalized Abel’s Integral Equation by Variational Iteration Method
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作者 R. N. Prajapati Rakesh Mohan Pankaj Kumar 《American Journal of Computational Mathematics》 2012年第4期312-315,共4页
In this paper, a user friendly algorithm based on the variational iteration method (VIM) is proposed to solve singular integral equations with generalized Abel’s kernel. It is observed that an approximate solutions y... In this paper, a user friendly algorithm based on the variational iteration method (VIM) is proposed to solve singular integral equations with generalized Abel’s kernel. It is observed that an approximate solutions yn(x) converges to the exact solution irrespective of the initial choice y0 (x). Illustrative numerical examples are given to demonstrate the efficiency and simplicity of the method in solving these types of singular integral equations. 展开更多
关键词 VARIATIONAL iteration Method sINGULAR Integral Equation Abel’s KERNEL
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Analytical Solution of Two Extended Model Equations for Shallow Water Waves by He’s Variational Iteration Method
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作者 Mehdi Safari Majid Safari 《American Journal of Computational Mathematics》 2011年第4期235-239,共5页
In this paper, we consider two extended model equations for shallow water waves. We use He’s variational iteration method (VIM) to solve them. It is proved that this method is a very good tool for shallow water wave ... In this paper, we consider two extended model equations for shallow water waves. We use He’s variational iteration method (VIM) to solve them. It is proved that this method is a very good tool for shallow water wave equations and the obtained solutions are shown graphically. 展开更多
关键词 He’s VARIATIONAL iteration Method sHALLOW Water Wave Equation
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Fixed-Point Existence and Approximation Theorem for Controllable Mapping with Mann Iterative Procedure
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作者 YANG Hansheng~1 ZHONG Shouming~2(1.Department of Mathematics,Southwest University of Science and Technology Sichuan Mianyang 621002 China 2.School of Applied Mathematics,UESTC Chengdu Sichuan 610054 China) 《Journal of Electronic Science and Technology of China》 2003年第1期87-89,共3页
The concept of controllable mapping,which is a kind of Lipschitzian mapping,is induced.In certain case,any controllable mapping,on a closed convex subset of Banach space,has at least onefixed point,and its Mann iterat... The concept of controllable mapping,which is a kind of Lipschitzian mapping,is induced.In certain case,any controllable mapping,on a closed convex subset of Banach space,has at least onefixed point,and its Mann iterative sequence converges strongly to the fixed point.Moreover,theestimation between the iterative sequence and the fixed point is,in sulface,as the same as in Banachcontractive mapping. 展开更多
关键词 controllable mapping Lipschitzian mapping fixed point mann iterative procedure
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Calculation of Combustion Products by the New Iteration Method of Non-linear Equations
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作者 Paramust Juntarakod Thanakom Soontomchainacksaeng 《Journal of Mathematics and System Science》 2013年第1期15-25,共11页
For a specific combustion problem involving calculations of several species at the equilibrium state, it is simpler to write a general computer program and calculate the combustion concentration. Original work describ... For a specific combustion problem involving calculations of several species at the equilibrium state, it is simpler to write a general computer program and calculate the combustion concentration. Original work describes, an adaptation of Newton-Raphson method was used for solving the highly nonlinear system of equations describing the formation of equilibrium products in reacting of fuel-additive-air mixtures. This study also shows what possible of the results. In this paper, to be present the efficient numerical algorithms for. solving the combustion problem, to be used nonlinear equations based on the iteration method and high order of the Taylor series. The modified Adomian decomposition method was applied to construct the numerical algorithms. Some numerical illustrations are given to show the efficiency of algorithms. Comparisons of results by the new Matlab routines and previous routines, the result data indicate that the new Matlab routines are reliable, typical deviations from previous results are less than 0.05%. 展开更多
关键词 Non-linear equation Newton-Raphson method Adomian decomposition method Householder's iteration method highorder iteration method chemical equilibrium fuel and combustion products.
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On the Equivalence of Implicit Kirk-Type Fixed Point Iteration Schemes for a General Class of Maps
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作者 Alfred Olufemi Bosede Hudson Akewe +1 位作者 Omolara Fatimah Bakre Ashiribo Senapon Wusu 《Journal of Applied Mathematics and Physics》 2019年第1期123-137,共15页
In this paper, a modified implicit Kirk-multistep iteration scheme and a strong convergence result for a general class of maps in a normed linear space was established. It was also shown that the convergence of this i... In this paper, a modified implicit Kirk-multistep iteration scheme and a strong convergence result for a general class of maps in a normed linear space was established. It was also shown that the convergence of this iteration scheme is equivalent to the convergency of some other implicit Kirk-type iteration (implicit Kirk-Noor, implicit Kirk-Ishikawa and implicit Kirk-Mann iterations) for the same class of maps. Some numerical examples were considered to show that the equivalence of convergence results to the fixed point is true. The results unify most equivalence results in literature. 展开更多
关键词 IMPLICIT Kirk-Multistep IMPLICIT Kirk-mann iterations strong Convergence EQUIVALENCE GENERAL CLAss of MAPs
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Existence of Monotone Positive Solution for a Fourth-Order Three-Point BVP with Sign-Changing Green’s Function
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作者 Junrui Yue Yun Zhang Qingyue Bai 《Open Journal of Applied Sciences》 2024年第1期63-69,共7页
This paper is concerned with the following fourth-order three-point boundary value problem , where , we discuss the existence of positive solutions to the above problem by applying to the fixed point theory in cones a... This paper is concerned with the following fourth-order three-point boundary value problem , where , we discuss the existence of positive solutions to the above problem by applying to the fixed point theory in cones and iterative technique. 展开更多
关键词 Fourth-Order Three-Point Boundary Value Problem sign-Changing Green’s Function Fixed Point Index iterative Technique Monotone Positive solution EXIsTENCE
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V/S和Mann-Kendall相结合的方法在洪涝灾情分析中的应用 被引量:8
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作者 孙东永 畅建霞 +1 位作者 黄强 王义民 《西北农林科技大学学报(自然科学版)》 CSCD 北大核心 2012年第4期230-234,共5页
【目的】将V/S分析法引入到洪涝灾害面积序列的长记忆性研究,为洪涝灾害的预测和防治提供参考。【方法】以洞庭湖1949-1998年50年的洪涝灾害面积序列为研究对象,采用V/S分析法计算其Hurst指数,并结合其Mann-Kendall趋势分析洪涝灾害面... 【目的】将V/S分析法引入到洪涝灾害面积序列的长记忆性研究,为洪涝灾害的预测和防治提供参考。【方法】以洞庭湖1949-1998年50年的洪涝灾害面积序列为研究对象,采用V/S分析法计算其Hurst指数,并结合其Mann-Kendall趋势分析洪涝灾害面积序列未来的变化趋势。【结果】20世纪70年代以来洞庭湖区的洪灾面积下降趋势明显,90年代以后涝灾面积上升趋势显著,洞庭湖洪涝灾害时间序列V/S分析的Hurst指数均大于0.5,表明洪涝灾害面积序列的变化趋势在未来将持续。【结论】V/S分析是一种有效的趋势预测方法。将V/S分析法与Mann-Kendall相结合的方法能够分析洪涝灾害时间序列未来的变化趋势,是一种有效的未来趋势预测方法。 展开更多
关键词 洪涝灾害 V/s分析 mann-KENDALL HURsT指数 变化趋势预测
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