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Arithmetic Mean

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Jumat Sulaiman – 1st expert on this subject based on the ideXlab platform

  • Half-Sweep Arithmetic Mean Method for Solving 2D Elliptic Equation
    International journal of applied mathematics and statistics, 2019
    Co-Authors: Azali Saudi, Jumat Sulaiman

    Abstract:

    This paper presents our study on combining the half-sweep iteration technique with the twostage Arithmetic Mean (AM) method namely Half-Sweep Arithmetic Mean (HSAM) method in solving 2D elliptic equation. Recently, the HSAM method was studied extensively since it was very suitable for parallel implementation on a multiprocessor system. In the previous works, its great potential was demonstrated in solving partial differential equations (PDEs) mainly in one dimensional space. In this study, several numerical experiments were carried out to examine the efficiency of the suggested HSAM method in solving PDEs in two dimensional space. The implementation of the Full-Sweep Arithmetic Mean (FSAM) method is also provided. For performance comparison, the implementations of the standad Full-Sweep Gauss-Seidel (FSGS) and Half-Sweep Gauss-Seidel (HSGS) methods are presented.

  • The Arithmetic Mean iterative method for solving 2D Helmholtz equation
    , 2014
    Co-Authors: Mohana Sundaram Muthuvalu, Jumat Sulaiman, Mohd Kamalrulzaman Md Akhir, Mohamed Suleiman, Sarat C. Dass, Narinderjit Singh Sawaran Singh

    Abstract:

    In this paper, application of the Arithmetic Mean (AM) iterative method is extended by solving second order finite difference algebraic equations. The performance of AM method in solving second order finite difference algebraic equations is comparatively studied by their application on two-dimensional Helmholtz equation. Numerical results of AM method in solving two test problems are included and compared with the standard Gauss-Seidel (GS) method. Based on the numerical results obtained, the results show that AM method is better than GS method in the sense of number of iterations and CPU time.

  • Solving first kind linear Fredholm integral equations with semi-smooth kernel using 2-point half-sweep block Arithmetic Mean method
    , 2013
    Co-Authors: Mohana Sundaram Muthuvalu, Elayaraja Aruchunan, Jumat Sulaiman

    Abstract:

    This paper investigates the application of the 2-Point Half-Sweep Block Arithmetic Mean (2-HSBLAM) iterative method with first order composite closed Newton-Cotes quadrature scheme for solving first kind linear Fredholm integral equations. The formulation and implementation of the method are presented. In addition, numerical results of test problems are also included to verify the performance of the method compared to existing Arithmetic Mean (AM) and 2-Point Full-Sweep Block Arithmetic Mean (2-FSBLAM) methods. From the numerical results, it is noticeable that the 2-HSBLAM method is superior than AM and 2-FSBLAM methods in terms of computational time.

Yan-kuen Wu – 2nd expert on this subject based on the ideXlab platform

  • On the Max-quasi-Arithmetic Mean Powers of a Fuzzy Matrix
    2009 International Joint Conference on Computational Sciences and Optimization, 2009
    Co-Authors: Yan-kuen Wu

    Abstract:

    Since Thomason’s paper in 1977 showing that the max-min powers of a fuzzy matrix either converge or oscillate with a finite period, many different algebraic operations are employed to explore the limiting behavior of powers of a fuzzy matrix, such as max-min/max-product/max-Archimedean t-norm/max-t-norm/max-Arithmetic Mean operations. In this article, we consider the max-quasi-Arithmetic Mean powers of a fuzzy matrix which is an extensive case of the max-Arithmetic Mean, max-root power Mean and max-convex Mean. We also show that the powers of such fuzzy matrices are always convergent. Some numerical examples are provided to show the situation of convergence.

  • CSO (2) – On the Max-quasi-Arithmetic Mean Powers of a Fuzzy Matrix
    2009 International Joint Conference on Computational Sciences and Optimization, 2009
    Co-Authors: Yan-kuen Wu

    Abstract:

    Since Thomason’s paper in 1977 showing that the max-min powers of a fuzzy matrix either converge or oscillate with a finite period, many different algebraic operations are employed to explore the limiting behavior of powers of a fuzzy matrix, such as max-min/max-product/max-Archimedean t-norm/max-t-norm/max-Arithmetic Mean operations. In this article, we consider the max-quasi-Arithmetic Mean powers of a fuzzy matrix which is an extensive case of the max-Arithmetic Mean, max-root power Mean and max-convex Mean. We also show that the powers of such fuzzy matrices are always convergent. Some numerical examples are provided to show the situation of convergence.

  • Convergence of powers for a fuzzy matrix with convex combination of max-min and max-Arithmetic Mean operations
    Information Sciences, 2009
    Co-Authors: Yan-kuen Wu

    Abstract:

    Fuzzy matrices have been proposed to represent fuzzy relations on finite universes. Since Thomason’s paper in 1977 showing that powers of a max-min fuzzy matrix either converge or oscillate with a finite period, conditions for limiting behavior of powers of a fuzzy matrix have been studied. It turns out that the limiting behavior depends on the algebraic operations employed, which usually in the literature includes max-min/max-product/max-Archimedean t-norm/max t-norm/max-Arithmetic Mean operations, respectively. In this paper, we consider the powers of a fuzzy matrix with convex combination of max-min and max-Arithmetic Mean operations. We show that the powers of such a fuzzy matrix are always convergent.

Kwang-cheng Chen – 3rd expert on this subject based on the ideXlab platform

  • Data extraction via histogram and Arithmetic Mean queries: Fundamental limits and algorithms
    2016 IEEE International Symposium on Information Theory (ISIT), 2016
    Co-Authors: I-hsiang Wang, Shao-lun Huang, Kwang-cheng Chen

    Abstract:

    The problems of extracting information from a data set via histogram queries or Arithmetic Mean queries are considered. We first show that the fundamental limit on the number of histogram queries, m, so that the entire data set of size n can be extracted losslessly, is m = Θ(n/log n), sub-linear in the size of the data set. For proving the lower bound (converse), we use standard arguments based on simple counting. For proving the upper bound (achievability), we proposed two query mechanisms. The first mechanism is random sampling, where in each query, the items to be included in the queried subset are uniformly randomly selected. With random sampling, it is shown that the entire data set can be extracted with vanishing error probability using Ω(n/log n) queries. The second one is a non-adaptive deterministic algorithm. With this algorithm, it is shown that the entire data set can be extracted exactly (no error) using Ω(n/log n) queries. We then extend the results to Arithmetic Mean queries, and show that for data sets taking values in a real-valued finite Arithmetic progression, the fundamental limit on the number of Arithmetic Mean queries to extract the entire data set is also Θ(n/log n).

  • ISIT – Data extraction via histogram and Arithmetic Mean queries: Fundamental limits and algorithms
    2016 IEEE International Symposium on Information Theory (ISIT), 2016
    Co-Authors: I-hsiang Wang, Shao-lun Huang, Kwang-cheng Chen

    Abstract:

    The problems of extracting information from a data set via histogram queries or Arithmetic Mean queries are considered. We first show that the fundamental limit on the number of histogram queries, m, so that the entire data set of size n can be extracted losslessly, is m = Θ(n/log n), sub-linear in the size of the data set. For proving the lower bound (converse), we use standard arguments based on simple counting. For proving the upper bound (achievability), we proposed two query mechanisms. The first mechanism is random sampling, where in each query, the items to be included in the queried subset are uniformly randomly selected. With random sampling, it is shown that the entire data set can be extracted with vanishing error probability using Ω(n/log n) queries. The second one is a non-adaptive deterministic algorithm. With this algorithm, it is shown that the entire data set can be extracted exactly (no error) using Ω(n/log n) queries. We then extend the results to Arithmetic Mean queries, and show that for data sets taking values in a real-valued finite Arithmetic progression, the fundamental limit on the number of Arithmetic Mean queries to extract the entire data set is also Θ(n/log n).