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Lin Xiao - One of the best experts on this subject based on the ideXlab platform.

  • a novel recurrent neural network and its finite time solution to time varying Complex Matrix inversion
    Neurocomputing, 2019
    Co-Authors: Lin Xiao, Yongsheng Zhang, Bolin Liao, Zhiguo Tan
    Abstract:

    Abstract A Complex-valued nonlinear recurrent neural network is designed and researched for time-varying Matrix inversion solving in Complex field. Unlike the design methods of the conventional gradient neural network (CGNN) and the previous Zhang neural network (ZNN), the proposed Complex-valued nonlinear recurrent neural network (CVNRNN) model is established on basis of a nonlinear evolution formula and possesses a better finite-time convergence Besides, the detailed theoretical analysis provides a guarantee for the finite-time convergence achievement of the CVNRNN model. In addition, the theoretical analysis is also verified by numerical simulations, which comparatively show that the proposed CVNRNN model is faster and more accurate than the ZNN model and the CGNN model in solving time-varying Complex Matrix inversion.

  • a finite time convergent neural dynamics for online solution of time varying linear Complex Matrix equation
    Neurocomputing, 2015
    Co-Authors: Lin Xiao
    Abstract:

    This paper proposes and investigates a finite-time convergent neural dynamics (FTCND) for online solution of time-varying linear Complex Matrix equation in Complex domain. Different from the conventional gradient-based neural dynamical method, the proposed method utilizes adequate time-derivative information of time-varying Complex Matrix coefficients. It is theoretically proved that our FTCND model can converge to the theoretical solution of time-varying linear Complex Matrix equation within finite time. In addition, the upper bound of the convergence time is derived analytically via Lyapunov theory. For comparative purposes, the conventional gradient-based neural dynamics (GND) is developed and exploited for solving such a time-varying Complex problem. Computer-simulation results verify the effectiveness and superiorness of the FTCND model for solving time-varying linear Complex Matrix equation in Complex domain, as compared with the GND model.

Anping Liao - One of the best experts on this subject based on the ideXlab platform.

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

  • the minimal norm least squares hermitian solution of the Complex Matrix equation axb cxd e
    Journal of The Franklin Institute-engineering and Applied Mathematics, 2018
    Co-Authors: Fengxia Zhang, Ying Li, Jianli Zhao
    Abstract:

    Abstract In this paper, by applying the real representations of Complex matrices, the particular structure of the real representations and the Moore–Penrose generalized inverse, we obtain the explicit expression of the minimal norm least squares Hermitian solution of the Complex Matrix equation A X B + C X D = E . And we also derive the minimal norm least squares Hermitian solution of the Complex Matrix equation A X B = E . Our proposed formulas only involve real matrices, and therefore are more effective and portable than those reported in Yuan and Liao (2014). The corresponding algorithms only perform real arithmetic which also consider the particular structure of the real representations of Complex matrices. Two numerical examples are provided to demonstrate the effectiveness of our algorithms.

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

  • bgwm as second constituent of Complex Matrix model
    Journal of High Energy Physics, 2009
    Co-Authors: A Alexandrov, A Mironov, A Morozov
    Abstract:

    In [1] we explained that partition functions of various Matrix models can be constructed from that of the cubic Kontsevich model, which, therefore, becomes a basic elementary building block in M-theory of Matrix models [2]. However, the less topical Complex Matrix model appeared to be an exception: its decomposition involved not only the Kontsevich ?-function but also another constituent, which we now identify as the Brezin-Gross-Witten (BGW) partition function. The BGW ?-function can be represented either as a generating function of all unitary-Matrix integrals or as a Kontsevich-Penner model with potential 1/X (instead of X3 in the cubic Kontsevich model).

  • bgwm as second constituent of Complex Matrix model
    arXiv: High Energy Physics - Theory, 2009
    Co-Authors: A Alexandrov, A Mironov, A Morozov
    Abstract:

    Earlier we explained that partition functions of various Matrix models can be constructed from that of the cubic Kontsevich model, which, therefore, becomes a basic elementary building block in "M-theory" of Matrix models. However, the less topical Complex Matrix model appeared to be an exception: its decomposition involved not only the Kontsevich tau-function but also another constituent, which we now identify as the Brezin-Gross-Witten (BGW) partition function. The BGW tau-function can be represented either as a generating function of all unitary-Matrix integrals or as a Kontsevich-Penner model with potential 1/X (instead of X^3 in the cubic Kontsevich model).

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