• Title, Summary, Keyword: Iteration

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REPULSIVE FIXED-POINTS OF THE LAGUERRE-LIKE ITERATION FUNCTIONS

  • Ham, YoonMee;Lee, Sang-Gu
    • Korean Journal of Mathematics
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    • v.16 no.1
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    • pp.51-55
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    • 2008
  • Let f be an analytic function with a simple zero in the reals or the complex numbers. An extraneous fixed-point of an iteration function is a fixed-point different from a zero of f. We prove that all extraneous fixed-points of Laguerre-like iteration functions and general Laguerre-like functions are repulsive.

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ON THE ON THE CONVERGENCE BETWEEN THE MANN ITERATION AND ISHIKAWA ITERATION FOR THE GENERALIZED LIPSCHITZIAN AND Φ-STRONGLY PSEUDOCONTRACTIVE MAPPINGS

  • Xue, Zhiqun
    • Bulletin of the Korean Mathematical Society
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    • v.45 no.4
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    • pp.635-644
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    • 2008
  • In this paper, we prove that the equivalence between the convergence of Mann and Ishikawa iterations for the generalized Lipschitzian and $\Phi$-strongly pseudocontractive mappings in real uniformly smooth Banach spaces. Our results significantly generalize the recent known results of [B. E. Rhoades and S. M. Soltuz, The equivalence of Mann iteration and Ishikawa iteration for non-Lipschitz operators, Int. J. Math. Math. Sci. 42 (2003), 2645.2651].

NUMBER OF VERTICES FOR POLYGONAL FUNCTIONS UNDER ITERATION

  • Li, Lin
    • The Pure and Applied Mathematics
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    • v.14 no.2
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    • pp.99-109
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    • 2007
  • Being complicated in computation, iteration of a nonlinear 1-dimensional mapping makes many interesting problems, one of which is about the change of the number of vertices under iteration. In this paper we investigate iteration of polygonal functions which each have only one vertex and give conditions under which the number of vertices either does not increase or has a bound under iteration.

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Variable Iteration Decoding Control Method for Iteration Codes (Iteration 부호의 가변반복복호 제어기법)

  • 백승재;이성우;박진수
    • Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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    • pp.753-757
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    • 2003
  • In this paper, We propose an efficient iteration decoding control method with variable iteration decoding for iteration codes decoding. As the number of iterations increases, the bit error rate and frame error rate of the decoder decrease and the incremental improvement gradually diminishes. However, as the iteration decoding number is increase, it require much delay and amount of processing for decoding. Thus we propose variable iteration control method to adapt variation of channel using Frame Error-Check indicator. Therefore, the CRC method requires the fewest iterations and less computation than the CE method and the SCR methods.

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STRONG CONVERGENCE THEOREMS FOR A QUASI CONTRACTIVE TYPE MAPPING EMPLOYING A NEW ITERATIVE SCHEME WITH AN APPLICATION

  • Chauhan, Surjeet Singh;Utreja, Kiran;Imdad, Mohammad;Ahmadullah, Md
    • Honam Mathematical Journal
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    • v.39 no.1
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    • pp.1-25
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    • 2017
  • In this paper, we introduce a new scheme namely: CUIA-iterative scheme and utilize the same to prove a strong convergence theorem for quasi contractive mappings in Banach spaces. We also establish the equivalence of our new iterative scheme with various iterative schemes namely: Picard, Mann, Ishikawa, Agarwal et al., Noor, SP, CR etc for quasi contractive mappings besides carrying out a comparative study of rate of convergences of involve iterative schemes. The present new iterative scheme converges faster than above mentioned iterative schemes whose detailed comparison carried out with the help of different tables and graphs prepared with the help of MATLAB.

A Study on the Acceleration of the Solution Convergence for the Rigid Plastic FEM (강소성 유한요소해석에서 해의 수렴 가속화에 관한 연구)

  • 최영
    • Proceedings of the Korean Society of Precision Engineering Conference
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    • pp.347-350
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    • 2004
  • In this paper, the acceleration is studied for the rigid-plastic FEM of metal forming simulation. In the FEM, the direct iteration and Newton-Raphson iteration are applied to obtain the initial solution and accurate solution respectively. In general, the acceleration scheme for the direct iteration is not used. In this paper, an Aitken accelerator is applied to the direct iteration. In the modified Newton-Raphson iteration, the step length or the deceleration coefficient is used for the fast and robust convergence. The step length can be determined by using the accelerator. The numerical experiments have been performed for the comparisons. The faster convergence is obtained with the acceleration in the direct and Newton-Raphson iterations.

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ITERATION PROCESSES WITH ERRORS FOR NONLINEAR EQUATIONS INVOLVING $\alpha$-STRONGLY ACCRETIVE OPERATORS IN BANACH SPACES

  • Jung, Jong-Soo
    • East Asian mathematical journal
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    • v.17 no.2
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    • pp.349-365
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    • 2001
  • Let X be a real Banach space and $A:X{\rightarrow}2^X$ be an $\alpha$-strongly accretive operator. It is proved that if the duality mapping J of X satisfies Condition (I) with additional conditions, then the Ishikawa and Mann iteration processes with errors converge strongly to the unique solution of operator equation $z{\in}Ax$. In addition, the convergence of the Ishikawa and Mann iteration processes with errors for $\alpha$-strongly pseudo-contractive operators is given.

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CONVERGENCE THEOREMS OF THREE-STEP ITERATION METHODS FOR QUASI-CONTRACTIVE MAPPINGS

  • Hao, Jinbiao;Wang, Li;Kang, Shin-Min;Shim, Soo-Hak
    • East Asian mathematical journal
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    • v.18 no.2
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    • pp.261-270
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    • 2002
  • We obtain the convergence of three-step iteration methods and generalized three-step iteration methods for quasi-contractive and generalized quasi-contractive mappings, respectively, in Banach spaces. Our results extend the corresponding results in [1], [4]-[6].

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ISHIKAWA AND MANN ITERATION METHODS FOR STRONGLY ACCRETIVE OPERATORS

  • JONG YEOUL PARK;JAE UG JEONG
    • Communications of the Korean Mathematical Society
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    • v.13 no.4
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    • pp.765-773
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    • 1998
  • Let E be a smooth Banach space. Suppose T : E longrightarrow E is a strongly accretive map. It is proved that each of the two well known fixed point iteration methods (the Mann and Ishikawa iteration methods), under suitable conditions, converges strongly to a solution of the equation Tx = f.

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ITERATION METHOD FOR CONSTRAINED OPTIMIZATION PROBLEMS GOVERNED BY PDE

  • Lee, Hyung-Chun
    • Communications of the Korean Mathematical Society
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    • v.13 no.1
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    • pp.195-209
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    • 1998
  • In this paper we present a new iteration method for solving optimization problems governed by partial differential equations. We generalize the existing methods such as simple gradient methods and pseudo-time methods to get an efficient iteration method. Numerical tests show that the convergence of the new iteration method is much faster than those of the pseudo-time methods especially when the parameter $\sigma$ in the cost functional is small.

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