Using shifted Legendre orthonormal polynomials for solving fractional optimal control problems [PDF]
Iranian Journal of Numerical Analysis and Optimization, 2022 shifted Legendre orthonormal polynomials (SLOPs) are used to approximate the numerical solutions of fractional optimal control problems. To do so, first, the operational matrix of the Caputo fractional derivative, the SLOPs, and Lagrange ...
R. Naseri, A. Heydari, A.S. Bagherzadeh
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Uniformly bounded orthonormal polynomials on the sphere [PDF]
Bulletin of the London Mathematical Society, 2015 Improved presentation and corrected ...
Marzo Sánchez, Jordi +1 more
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Approximation of functions in Hölder’s class and solution of nonlinear Lane–Emden differential equation by orthonormal Euler wavelets [PDF]
Iranian Journal of Numerical Analysis and OptimizationIn this article, a method has been developed for the solution of a non-linear Lane-Emden differential equation based on orthonormal Euler wavelet series.
H.C. Yadav, A. Yadav, S. Lal
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Derivatives of Integrating Functions for Orthonormal Polynomials with Exponential-Type Weights
Journal of Inequalities and Applications, 2009 Let wρ(x):=|x|ρexp(−Q(x)), ρ>−1/2, where Q∈C2:(−∞,∞)→[0,∞) is an even function.
Hee Sun Jung, Ryozi Sakai
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Stable Calculation of Krawtchouk Functions from Triplet Relations
Mathematics, 2021 Deployment of the recurrence relation or difference equation to generate discrete classical orthogonal polynomials is vulnerable to error propagation. This issue is addressed for the case of Krawtchouk functions, i.e., the orthonormal basis derived from ...
Albertus C. den Brinker
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New Operational Matrices of Seventh Degree Orthonormal Bernstein Polynomials
مجلة بغداد للعلوم, 2015 Based on analyzing the properties of Bernstein polynomials, the extended orthonormal Bernstein polynomials, defined on the interval [0, 1] for n=7 is achieved. Another method for computing operational matrices of derivative and integration D_b and R_(n+1)
Baghdad Science Journal
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The Sufficient Conditions for Orthogonal Matching Pursuit to Exactly Reconstruct Sparse Polynomials
Mathematics, 2022 Orthogonal matching pursuit (OMP for short) is a classical method for sparse signal recovery in compressed sensing. In this paper, we consider the application of OMP to reconstruct sparse polynomials generated by uniformly bounded orthonormal systems ...
Aitong Huang, Renzhong Feng, Andong Wang
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Calculating Bivariate Orthonormal Polynomials By Recurrence
Australian & New Zealand Journal of Statistics, 2013 SummaryEmerson gave recurrence formulae for the calculation of orthonormal polynomials for univariate discrete random variables. He claimed that as these were based on the Christoffel–Darboux recurrence relation they were more efficient than those based on the Gram–Schmidt method.
Rayner, J. C. W. +3 more
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Collocation Orthonormal Bernstein Polynomials Method for Solving Integral Equations [PDF]
Engineering and Technology Journal, 2015 In this paper, we use a combination of Orthonormal Bernstein functions on the interval [0,1] for degree m=5,and 6 to produce anew approach implementing Bernstein operational matrix of derivative as a method for the numerical solution of linear Fredholm ...
Suha. N. Shihab +2 more
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Orthonormal polynomial wavelets on the interval [PDF]
Proceedings of the American Mathematical Society, 2005 We use special functions and orthonormal wavelet bases on the real line to construct wavelet-like bases. With these wavelets we can construct polynomial bases on the interval; moreover, we can use them for the numerical resolution of degenerate elliptic operators.
Dai, Dao-Qing, Lin, Wei
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