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32 results for “linear algebra”
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Research ArticleOpen accessIn the abstractOn Gröbner Bases and Their Uses in Solving System of Polynomial Equations and Graph ColoringHaridas Kumar Das, Nasim RezaThis paper is based on the analytic and computational solution procedures of Gröbner basis and its applications. We show the behavior of the ideals generated by polynomials from a polynomial ring. We also present the idea of a zero dimensional ideal and use of this ideal to solve system of polynomial equations. We then introduce an algorithmic procedure for solving … …Journal of Mathematics and Statistics, Vol. 14, Issue 1 · 27 Jun 2018 · 8,591 accessesView PDFCite
Research ArticleOpen accessIn the abstractA Computational Method Based on Bernstein Polynomials for Solving FredholmIntegro-Differential Equations under Mixed ConditionsMiloud Moussai, Lakhdar ChiterIn this study, a computational method for solving linear FredholmIntegro-Differential Equation (FIDE) of the first order under the mixed conditions using the Bernstein polynomials. First, we present some properties of these polynomials and the method is explained. These properties are then used to convert the integro-differential equation to a system of linear algebraic equations with unknown Bernstein coefficients. Using Galerkin … …Journal of Mathematics and Statistics, Vol. 13, Issue 1 · 27 Feb 2017 · 7,142 accessesView PDFCite
Research ArticleOpen accessIn the abstractMinimization of ℓ2-Norm of the KSOR OperatorA. I. Alzaki, I. K. YoussefWe consider the problem of minimizing the ℓ2-norm of the KSOR operator when solving a linear systems of the form AX = b where, A = I +B (TJ = -B, is the Jacobi iteration matrix), B is skew symmetric matrix. Based on the eigenvalue functional relations given for the KSOR method, we find optimal values of the relaxation parameter … …Journal of Mathematics and Statistics, Vol. 8, Issue 4 · 8 Jan 2013 · 7,083 accessesView PDFCite
Research ArticleOpen accessIn the abstractOn the Successive Overrelaxation MethodI. K. YoussefProblem statement: A new variant of the Successive Overrelaxation (SOR) method for solving linear algebraic systems, the KSOR method was introduced. The treatment depends on the assumption that the current component can be used simultaneously in the evaluation in addition to the use the most recent calculated components as in the SOR method. Approach: Using the hidden explicit characterization of … …Journal of Mathematics and Statistics, Vol. 8, Issue 2 · 22 Feb 2012 · 12,799 accessesView PDFCite
Research ArticleOpen accessIn the abstractSome Applications of Spanning Trees in Complete and Complete Bipartite GraphsS. N. DaoudProblem statement: The number of spanning trees τ(G) in graphs (networks) is an important invariant, it is also an important measure of reliability of a network. Approach: Using linear algebra and matrix analysis techniques to evaluate the associated determinants. Results: In this study we derive simple formulas for the number of spanning trees of complete graph Kn and complete bipartite … …American Journal of Applied Sciences, Vol. 9, Issue 4 · 15 Feb 2012 · 7,263 accessesView PDFCite
Research ArticleOpen accessIn the abstractComplexity of Cocktail Party Graph and Crown GraphS. N. DaoudProblem statement: The number of spanning trees τ(G) in graphs (networks) was an important invariant. Approach: Using the properties of the Chebyshev polynomials of the second kind and the linear algebra techniques to evaluate the associated determinants. Results: The complexity, number of spanning trees, of the cocktail party graph on 2n vertices, given in detail in the text was proved. … …American Journal of Applied Sciences, Vol. 9, Issue 2 · 12 Dec 2011 · 7,868 accessesView PDFCite
Research ArticleOpen accessIn the abstractA Cryptosystem Using the Concepts of Algebraic Geometric CodeK. V. Pramod, C. ManjuProblem statement: Cryptosystem using linear codes was developed in 1978 by Mc-Eliece. Later in 1985 Niederreiter and others developed a modified version of cryptosystem using concepts of linear codes. But these systems were not used frequently because of its larger key size. In this study we were designing a cryptosystem using the concepts of algebraic geometric codes with smaller key … …Journal of Computer Science, Vol. 6, Issue 3 · 31 Mar 2010 · 7,444 accessesView PDFCite
Research ArticleOpen accessIn the abstractOn Calculating the Hougaard Measure of Skewness in a Nonlinear Regression Model with Two ParametersS. A. EL-ShehawyProblem statement: This study presented an alternative computational algorithm for determining the values of the Hougaard measure of skewness as a nonlinearity measure in a Nonlinear Regression model (NLR-model) with two parameters. Approach: These values indicated a degree of a nonlinear behavior in the estimator of the parameter in a NLR-model. Results: We applied the suggested algorithm on an example … …Journal of Mathematics and Statistics, Vol. 5, Issue 4 · 31 Dec 2009 · 7,159 accessesView PDFCite
Research ArticleOpen accessIn the abstractEOS: Evolutionary Overlay Service in Peer-to-Peer SystemsL. I. Zhijun, Liao MinghongThe peer-to-peer (P2P) systems nowadays can be mainly classified into two categories: structured and structure-less systems based on their overlay organization. The structured systems can achieve determinate efficiency due to their rigorous structure with the cost of losing robustness and vice versa. We provide a semi-structured overlay based on the separation of routing structures and overlay organizations in this paper … …American Journal of Applied Sciences, Vol. 2, Issue 10 · 31 Oct 2005 · 6,349 accessesView PDFCite
Research ArticleOpen accessIn the abstractq-Deformed Statistics from Position-Dependent Mass Schrödinger EquationaJesus Morales Rivas, Jose Juan Peña Gil, J. García RaveloAn algebraic approach is used to obtain the canonical form of the position-dependent mass Schrödinger equation from where a couple of canonical quantum variables, the q-deformed operators for the position xq, and the hermitian linear momentum operator pq are derived. In this q-deformed coordinate space, the commutator remains invariant namely [xq, pq] = iħ. By taking advantage of these q-deformed … …Journal of Mathematics and Statistics, Vol. 19, Issue 1 · 15 Sep 2023 · 5,191 accessesView PDFCite