Accumulation Point

14,000,000 Leading Edge Experts on the ideXlab platform

Scan Science and Technology

Contact Leading Edge Experts & Companies

Scan Science and Technology

Contact Leading Edge Experts & Companies

The Experts below are selected from a list of 4485 Experts worldwide ranked by ideXlab platform

Cornelis Roos - One of the best experts on this subject based on the ideXlab platform.

  • Convergence of Full-Newton Step Infeasible Interior-Point Methods for Linear Optimization
    2020
    Co-Authors: A. Asadi, G. Gu, Cornelis Roos
    Abstract:

    Roos [SIAM J. Optim., 16(4):1110‐1136, 2006] proposed a new primal-dual infeasible interior-Point method for Linear Optimization. This method can be viewed as a homotopy method, which diers from the classical infeasible interior-Point methods in that the new method uses only full-Newton steps (instead of damped steps). In this paper we investigate convergence properties of this method. We show that the homotopy path has precisely one Accumulation Point in the optimal set. Moreover, this Accumulation Point is the analytic center of a subset of the optimal set and depends on the starting Point of the infeasible interior-Point method.

  • Convergence of the homotopy path for a full-Newton step infeasible interior-Point method
    Operations Research Letters, 2010
    Co-Authors: A. Asadi, G. Gu, Cornelis Roos
    Abstract:

    Roos [C. Roos, A full-Newton step O(n) infeasible interior-Point algorithm for linear optimization. SIAM J. Optim. 16 (4) (2006) 1110-1136 (electronic)] proposed a new primal-dual infeasible interior-Point method for linear optimization. This new method can be viewed as a homotopy method. In this work, we show that the homotopy path has precisely one Accumulation Point in the optimal set. Moreover, this Accumulation Point is the analytic center of a subset of the optimal set and depends on the starting Point of the infeasible interior-Point method.

Yuqiu Zhao - One of the best experts on this subject based on the ideXlab platform.

  • Uniform asymptotics for discrete orthogonal polynomials on infinite nodes with an Accumulation Point
    Analysis and Applications, 2016
    Co-Authors: Xiaobo Wu, Shuaixia Xu, Yuqiu Zhao
    Abstract:

    In this paper, we develop the Riemann–Hilbert method to study the asymptotics of discrete orthogonal polynomials on infinite nodes with an Accumulation Point. To illustrate our method, we consider the Tricomi–Carlitz polynomials [Formula: see text] where [Formula: see text] is a positive parameter. Uniform Plancherel–Rotach type asymptotic formulas are obtained in the entire complex plane including a neighborhood of the origin, and our results agree with the ones obtained earlier in [W. M. Y. Goh and J. Wimp, On the asymptotics of the Tricomi–Carlitz polynomials and their zero distribution. I, SIAM J. Math. Anal. 25 (1994) 420–428] and in [K. F. Lee and R. Wong, Uniform asymptotic expansions of the Tricomi–Carlitz polynomials, Proc. Amer. Math. Soc. 138 (2010) 2513–2519].

  • uniform asymptotics for discrete orthogonal polynomials on infinite nodes with an Accumulation Point
    Analysis and Applications, 2016
    Co-Authors: Xiaobo Wu, Shuaixia Xu, Yuqiu Zhao
    Abstract:

    In this paper, we develop the Riemann–Hilbert method to study the asymptotics of discrete orthogonal polynomials on infinite nodes with an Accumulation Point. To illustrate our method, we consider the Tricomi–Carlitz polynomials fn(α)(z) where α is a positive parameter. Uniform Plancherel–Rotach type asymptotic formulas are obtained in the entire complex plane including a neighborhood of the origin, and our results agree with the ones obtained earlier in [W. M. Y. Goh and J. Wimp, On the asymptotics of the Tricomi–Carlitz polynomials and their zero distribution. I, SIAM J. Math. Anal. 25 (1994) 420–428] and in [K. F. Lee and R. Wong, Uniform asymptotic expansions of the Tricomi–Carlitz polynomials, Proc. Amer. Math. Soc. 138 (2010) 2513–2519].

  • uniform asymptotics for discrete orthogonal polynomials on infinite nodes with an Accumulation Point
    arXiv: Classical Analysis and ODEs, 2014
    Co-Authors: Xiaobo Wu, Shuaixia Xu, Yuqiu Zhao
    Abstract:

    In this paper, we develop the Riemann-Hilbert method to study the asymptotics of discrete orthogonal polynomials on infinite nodes with an Accumulation Point. To illustrate our method, we consider the Tricomi-Carlitz polynomials $f_n^{(\alpha)}(z)$ where $\alpha$ is a positive parameter. Uniform Plancherel-Rotach type asymptotic formulas are obtained in the entire complex plane including a neighborhood of the origin, and our results agree with the ones obtained earlier in [{\it SIAM J.\;Math.\;Anal} {\bf 25} (1994)] and [{{\it Proc.\;Amer.\;Math.\;Soc.\,}{\bf138} (2010)}].

O B Isaeva - One of the best experts on this subject based on the ideXlab platform.

  • period tripling Accumulation Point for complexified henon map
    arXiv: Chaotic Dynamics, 2005
    Co-Authors: O B Isaeva, Sergey P Kuznetsov
    Abstract:

    Accumulation Point of period-tripling bifurcations for complexified Henon map is found. Universal scaling properties of parameter space and Fourier spectrum intrinsic to this critical Point is demonstrated.

  • Properties of Fourier spectrum of the signal, generated at the Accumulation Point of period-tripling bifurcations
    arXiv: Chaotic Dynamics, 2005
    Co-Authors: O B Isaeva
    Abstract:

    Universal regularities of the Fourier spectrum of signal, generated by complex analytic map at the period-tripling bifurcations Accumulation Point are considered. The difference between intensities of the subharmonics at the values of frequency corresponding to the neighbor hierarchical levels of the spectrum is characterized by a constant $\gamma=21.9$ dB?, which is an analogue of the known value $\gamma_F=13.4$ dB, intrinsic to the Feigenbaum critical Point. Data of the physical experiment, directed to the observation of the spectrum at period-tripling Accumulation Point, are represented.

  • effect of noise on the dynamics of a complex map at the period tripling Accumulation Point
    Physical Review E, 2004
    Co-Authors: O B Isaeva, Sergey P Kuznetsov, A H Osbaldestin
    Abstract:

    As shown recently [O.B. Isaeva et al., Phys. Rev. E 64, 055201 (2001)], the phenomena intrinsic to dynamics of complex analytic maps under appropriate conditions may occur in physical systems. We study scaling regularities associated with the effect of additive noise upon the period-tripling bifurcation cascade generalizing the renormalization group approach of Crutchfield et al. [Phys. Rev. Lett. 46, 933 (1981)] and Shraiman et al. [Phys. Rev. Lett. 46, 935 (1981)], originally developed for the period doubling transition to chaos in the presence of noise. The universal constant determining the rescaling rule for the intensity of the noise in period tripling is found to be γ=12.206 640 9… . Numerical evidence of the expected scaling is demonstrated.

  • Effect of noise on the dynamics of a complex map at the period-tripling Accumulation Point.
    Physical review. E Statistical nonlinear and soft matter physics, 2004
    Co-Authors: O B Isaeva, Sergey P Kuznetsov, A H Osbaldestin
    Abstract:

    As shown recently [O.B. Isaeva et al., Phys. Rev. E 64, 055201 (2001)], the phenomena intrinsic to dynamics of complex analytic maps under appropriate conditions may occur in physical systems. We study scaling regularities associated with the effect of additive noise upon the period-tripling bifurcation cascade generalizing the renormalization group approach of Crutchfield et al. [Phys. Rev. Lett. 46, 933 (1981)] and Shraiman et al. [Phys. Rev. Lett. 46, 935 (1981)], originally developed for the period doubling transition to chaos in the presence of noise. The universal constant determining the rescaling rule for the intensity of the noise in period tripling is found to be gamma=12.206 640 9 em leader. Numerical evidence of the expected scaling is demonstrated.

  • Scaling properties in dynamics of non-analytic complex maps near the Accumulation Point of the period-tripling cascade
    arXiv: Chaotic Dynamics, 2001
    Co-Authors: O B Isaeva, Sergey P Kuznetsov
    Abstract:

    The Accumulation Point of the period-tripling bifurcation cascade in complex quadratic map was discovered by Golberg, Sinai, and Khanin (Russ.Math.Surv. 38:1, 1983, 187), and independently by Cvitanovic and Myrheim (Phys.Lett. A94:8, 1983, 329). As we argue, in the extended parameter space of smooth maps, not necessary satisfying the Cauchy - Riemann equations, the scaling properties associated with the period-tripling are governed by two relevant universal complex constants. The first one is $\delta_1 = 4.6002-8.9812i$ (in accordance with the mentioned works), while the other one, responsible for the violation of the analyticity, is found to be $\delta_2 = 2.5872+1.8067i$. It means that in the extended parameter space the critical behaviour associated with the period-tripling cascade is a phenomenon of codimension four. Scaling properties of the parameter space are illustrated by diagrams in special local coordinates. We emphasize a necessity for a nonlinear parameter change to observe the parameter space scaling.

A. Asadi - One of the best experts on this subject based on the ideXlab platform.

  • Convergence of Full-Newton Step Infeasible Interior-Point Methods for Linear Optimization
    2020
    Co-Authors: A. Asadi, G. Gu, Cornelis Roos
    Abstract:

    Roos [SIAM J. Optim., 16(4):1110‐1136, 2006] proposed a new primal-dual infeasible interior-Point method for Linear Optimization. This method can be viewed as a homotopy method, which diers from the classical infeasible interior-Point methods in that the new method uses only full-Newton steps (instead of damped steps). In this paper we investigate convergence properties of this method. We show that the homotopy path has precisely one Accumulation Point in the optimal set. Moreover, this Accumulation Point is the analytic center of a subset of the optimal set and depends on the starting Point of the infeasible interior-Point method.

  • Convergence of the homotopy path for a full-Newton step infeasible interior-Point method
    Operations Research Letters, 2010
    Co-Authors: A. Asadi, G. Gu, Cornelis Roos
    Abstract:

    Roos [C. Roos, A full-Newton step O(n) infeasible interior-Point algorithm for linear optimization. SIAM J. Optim. 16 (4) (2006) 1110-1136 (electronic)] proposed a new primal-dual infeasible interior-Point method for linear optimization. This new method can be viewed as a homotopy method. In this work, we show that the homotopy path has precisely one Accumulation Point in the optimal set. Moreover, this Accumulation Point is the analytic center of a subset of the optimal set and depends on the starting Point of the infeasible interior-Point method.

Xiaobo Wu - One of the best experts on this subject based on the ideXlab platform.

  • Uniform asymptotics for discrete orthogonal polynomials on infinite nodes with an Accumulation Point
    Analysis and Applications, 2016
    Co-Authors: Xiaobo Wu, Shuaixia Xu, Yuqiu Zhao
    Abstract:

    In this paper, we develop the Riemann–Hilbert method to study the asymptotics of discrete orthogonal polynomials on infinite nodes with an Accumulation Point. To illustrate our method, we consider the Tricomi–Carlitz polynomials [Formula: see text] where [Formula: see text] is a positive parameter. Uniform Plancherel–Rotach type asymptotic formulas are obtained in the entire complex plane including a neighborhood of the origin, and our results agree with the ones obtained earlier in [W. M. Y. Goh and J. Wimp, On the asymptotics of the Tricomi–Carlitz polynomials and their zero distribution. I, SIAM J. Math. Anal. 25 (1994) 420–428] and in [K. F. Lee and R. Wong, Uniform asymptotic expansions of the Tricomi–Carlitz polynomials, Proc. Amer. Math. Soc. 138 (2010) 2513–2519].

  • uniform asymptotics for discrete orthogonal polynomials on infinite nodes with an Accumulation Point
    Analysis and Applications, 2016
    Co-Authors: Xiaobo Wu, Shuaixia Xu, Yuqiu Zhao
    Abstract:

    In this paper, we develop the Riemann–Hilbert method to study the asymptotics of discrete orthogonal polynomials on infinite nodes with an Accumulation Point. To illustrate our method, we consider the Tricomi–Carlitz polynomials fn(α)(z) where α is a positive parameter. Uniform Plancherel–Rotach type asymptotic formulas are obtained in the entire complex plane including a neighborhood of the origin, and our results agree with the ones obtained earlier in [W. M. Y. Goh and J. Wimp, On the asymptotics of the Tricomi–Carlitz polynomials and their zero distribution. I, SIAM J. Math. Anal. 25 (1994) 420–428] and in [K. F. Lee and R. Wong, Uniform asymptotic expansions of the Tricomi–Carlitz polynomials, Proc. Amer. Math. Soc. 138 (2010) 2513–2519].

  • uniform asymptotics for discrete orthogonal polynomials on infinite nodes with an Accumulation Point
    arXiv: Classical Analysis and ODEs, 2014
    Co-Authors: Xiaobo Wu, Shuaixia Xu, Yuqiu Zhao
    Abstract:

    In this paper, we develop the Riemann-Hilbert method to study the asymptotics of discrete orthogonal polynomials on infinite nodes with an Accumulation Point. To illustrate our method, we consider the Tricomi-Carlitz polynomials $f_n^{(\alpha)}(z)$ where $\alpha$ is a positive parameter. Uniform Plancherel-Rotach type asymptotic formulas are obtained in the entire complex plane including a neighborhood of the origin, and our results agree with the ones obtained earlier in [{\it SIAM J.\;Math.\;Anal} {\bf 25} (1994)] and [{{\it Proc.\;Amer.\;Math.\;Soc.\,}{\bf138} (2010)}].