6 articles for “orthogonal polynomials”

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Research ArticleOpen accessIn the keywordsThe Numerical Computation of Rational Structures and Asymptotic Standard Deviations in Causal Time Series DataConcepción González-Concepción, María Candelaria Gil-Fariña, Celina Pestano-GabinoProblem statement: The specific properties of data series are of primary importance in several sciences. In the field of time series analysis, several researchers have considered the rational approximation theory, particularly the Padé Approximation and Orthogonal Polynomials. Approach: In this study, an approach for the statistical significance of two numerical methods, the r-s and q-d algorithm, was proposed which made … …Journal of Mathematics and Statistics, Vol. 5, Issue 3 · 30 Sep 2009 · 7,049 accessesView PDF Cite

Research ArticleOpen accessIn the keywordsClosed Form Solution to an Optimal Control Problem by Orthogonal Polynomial ExpansionMohammad Ali Tavallaei, Behrouz TousiIn this study the use of orthogonal polynomials for obtaining a close form solution to optimal control problems with a weighed quadratic cost function, is proposed. The method consists of using the Orthogonal Polynomials for the expansion of the state variables and the control signal. This expansion results in a set of linear equations, from which the closed form solution … …American Journal of Engineering and Applied Sciences, Vol. 1, Issue 2 · 30 Jun 2008 · 7,326 accessesView PDF Cite

Research ArticleOpen accessIn the keywordsHalf-bounded Numerical Solution of Singular Integral Equations with Cauchy KernelM. Abdulkawi, Z. K. Eshkuvatov, N.M.A. Nik LongProblem statement: In this study, a numerical solution for singular integral equations of the first kind with Cauchy kernel over the finite segment [-1,1] is presented. The numerical solution is bounded at x =1 and unbounded at x = -1. Approach: The numerical solution is derived by approximating the unknown density function using the weighted Chebyshev polynomials of the fourth … …Journal of Mathematics and Statistics, Vol. 7, Issue 1 · 25 Mar 2011 · 7,269 accessesView PDF Cite

Research ArticleOpen accessIn the keywordsOn Discrete Least Squares Polynomial Fit, Linear Spaces and Data ClassificationFrançois Dubeau, Youness MirThe best discrete least squares polynomial fit to a data set is revisited. We point out some properties related to the best polynomial and precise the dimension of vector spaces encountered to solve the problem. Finally, we suggest a basic classification of data sets based on their increasing or decreasing trend, and on their convexity or concavity form. …Journal of Mathematics and Statistics, Vol. 3, Issue 4 · 31 Dec 2007 · 6,865 accessesView PDF Cite

Research ArticleOpen accessIn the abstractWavelet Analysis and Orthogonal Moments based Classification of Microcalcification in Digital MammogramsN. V.S. Sree Rathna Lakshmi, C. ManoharanProblem statement: An important early sign of breast cancer is the clusters of micro calcifications in digital mammograms. To assist radiologists in the diagnosis of mammographic clusters a novel hybrid algorithm has been developed. Approach: A method, for detecting micro calcification in mammograms based on combined feature set with Ant Colony Optimization (ACO) was proposed. The diagonal matrix ‘S’ obtained … …Journal of Computer Science, Vol. 7, Issue 10 · 6 Aug 2011 · 6,558 accessesView PDF Cite

Research ArticleOpen accessAll words, across the recordOn the General Solution of First-Kind Hypersingular Integral EquationsSuzan J. Obaiys, Z. Abbas, N. M.A. Nik Long et al.A new algorithm is presented to provide a general solution for a first type Hyper singular Integral Equation (HSIE). The singular integral has been converted into a regular form by cancelling the singularity and then transforming it into a system of algebraic equation based orthogonal poly- nomials. We applied the convergence method presented by (Obaiys, 2013) to conform the numerical … …American Journal of Engineering and Applied Sciences, Vol. 9, Issue 2 · 28 Jan 2016 · 8,699 accessesView PDF Cite