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

HalfSweep Arithmetic Mean Method for Solving 2D Elliptic Equation
International journal of applied mathematics and statistics, 2019CoAuthors: Azali Saudi, Jumat SulaimanAbstract:This paper presents our study on combining the halfsweep iteration technique with the twostage Arithmetic Mean (AM) method namely HalfSweep 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 FullSweep Arithmetic Mean (FSAM) method is also provided. For performance comparison, the implementations of the standad FullSweep GaussSeidel (FSGS) and HalfSweep GaussSeidel (HSGS) methods are presented.

The Arithmetic Mean iterative method for solving 2D Helmholtz equation
, 2014CoAuthors: Mohana Sundaram Muthuvalu, Jumat Sulaiman, Mohd Kamalrulzaman Md Akhir, Mohamed Suleiman, Sarat C. Dass, Narinderjit Singh Sawaran SinghAbstract: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 twodimensional Helmholtz equation. Numerical results of AM method in solving two test problems are included and compared with the standard GaussSeidel (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 semismooth kernel using 2point halfsweep block Arithmetic Mean method
, 2013CoAuthors: Mohana Sundaram Muthuvalu, Elayaraja Aruchunan, Jumat SulaimanAbstract:This paper investigates the application of the 2Point HalfSweep Block Arithmetic Mean (2HSBLAM) iterative method with first order composite closed NewtonCotes 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 2Point FullSweep Block Arithmetic Mean (2FSBLAM) methods. From the numerical results, it is noticeable that the 2HSBLAM method is superior than AM and 2FSBLAM methods in terms of computational time.
Yankuen Wu – 2nd expert on this subject based on the ideXlab platform

On the MaxquasiArithmetic Mean Powers of a Fuzzy Matrix
2009 International Joint Conference on Computational Sciences and Optimization, 2009CoAuthors: Yankuen WuAbstract:Since Thomason’s paper in 1977 showing that the maxmin 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 maxmin/maxproduct/maxArchimedean tnorm/maxtnorm/maxArithmetic Mean operations. In this article, we consider the maxquasiArithmetic Mean powers of a fuzzy matrix which is an extensive case of the maxArithmetic Mean, maxroot power Mean and maxconvex 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 MaxquasiArithmetic Mean Powers of a Fuzzy Matrix
2009 International Joint Conference on Computational Sciences and Optimization, 2009CoAuthors: Yankuen WuAbstract:Since Thomason’s paper in 1977 showing that the maxmin 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 maxmin/maxproduct/maxArchimedean tnorm/maxtnorm/maxArithmetic Mean operations. In this article, we consider the maxquasiArithmetic Mean powers of a fuzzy matrix which is an extensive case of the maxArithmetic Mean, maxroot power Mean and maxconvex 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 maxmin and maxArithmetic Mean operations
Information Sciences, 2009CoAuthors: Yankuen WuAbstract:Fuzzy matrices have been proposed to represent fuzzy relations on finite universes. Since Thomason’s paper in 1977 showing that powers of a maxmin 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 maxmin/maxproduct/maxArchimedean tnorm/max tnorm/maxArithmetic Mean operations, respectively. In this paper, we consider the powers of a fuzzy matrix with convex combination of maxmin and maxArithmetic Mean operations. We show that the powers of such a fuzzy matrix are always convergent.
Kwangcheng 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), 2016CoAuthors: Ihsiang Wang, Shaolun Huang, Kwangcheng ChenAbstract: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), sublinear 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 nonadaptive 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 realvalued 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), 2016CoAuthors: Ihsiang Wang, Shaolun Huang, Kwangcheng ChenAbstract: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), sublinear 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 nonadaptive 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 realvalued 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).