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Illumination by Taylor polynomials
International Journal of Mathematics and Mathematical Sciences, 2001 Let f(x) be a differentiable function on the real line ℝ, and let P be a point not on the graph of f(x). Define the illumination index of P to be the number of distinct tangents to the graph of f which pass through P.
Alan Horwitz
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Taylor Polynomials of Rational Functions
Acta Mathematica Vietnamica, 2023 A Taylor variety consists of all fixed order Taylor polynomials of rational functions, where the number of variables and degrees of numerators and denominators are fixed. In one variable, Taylor varieties are given by rank constraints on Hankel matrices. Inversion of the natural parametrization is known as Padé approximation. We study the dimension and
Aldo Conca +2 more
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Fractal and Fractional, 2022 This paper proposes an accurate numerical approach for computing the solution of two-dimensional fractional Volterra integral equations. The operational matrices of fractional integration based on the Hybridization of block-pulse and Taylor polynomials ...
Antonio M Lopes +2 more
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Taylor Polynomials in a High Arithmetic Precision as Universal Approximators
ComputationFunction approximation is a fundamental process in a variety of problems in computational mechanics, structural engineering, as well as other domains that require the precise approximation of a phenomenon with an analytic function. This work demonstrates
Nikolaos Bakas
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Applications of q-Borel distribution series involving q-Gegenbauer polynomials to subclasses of bi-univalent functions [PDF]
HeliyonThis study introduces a new class of bi-univalent functions in the open disk using q-Borel distribution series and q-Gegenbauer polynomials. It provides estimates for the Taylor coefficients |μ2| and |μ3| for this family of functions, as well as ...
T. Al-Hawary +5 more
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Solutions of Fredholm integro-differential equations by using a hybrid of block-pulse functions and Taylor polynomials [PDF]
Songklanakarin Journal of Science and Technology (SJST), 2021 In this paper, we present numerical method for solving integro-differential equations of fractional order based on a hybrid of block-pulse functions and Taylor polynomials. Fractional derivative is described in the Caputo sense. Some numerical examples
Nattinee Khongnual, Weerachai Thadee
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Mathematics, 2023 Subclasses of analytic and bi-univalent functions have been extensively improved and utilized for estimating the Taylor–Maclaurin coefficients and the Fekete–Szegö functional.
Abdulmtalb Hussen, Abdelbaset Zeyani
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Efficient Evaluation of Matrix Polynomials beyond the Paterson–Stockmeyer Method
Mathematics, 2021 Recently, two general methods for evaluating matrix polynomials requiring one matrix product less than the Paterson–Stockmeyer method were proposed, where the cost of evaluating a matrix polynomial is given asymptotically by the total number of matrix ...
Jorge Sastre, Javier Ibáñez
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Nonlinear Engineering, 2023 Recently solving integro-differential equations have been the focus of attention among many researchers in the field of mathematic and engineering.
Ayati Zainab, Pourjafar Sadegh
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Formal Verification of Medina's Sequence of Polynomials for Approximating Arctangent [PDF]
Electronic Proceedings in Theoretical Computer Science, 2014 The verification of many algorithms for calculating transcendental functions is based on polynomial approximations to these functions, often Taylor series approximations. However, computing and verifying approximations to the arctangent function are very
Ruben Gamboa, John Cowles
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