Results 1 to 10 of about 11,041 (298)

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
Conca, Aldo, Naldi, Simone, Ottaviani, Giorgio, Sturmfels, Bernd   +3 more
openaire   +3 more sources

Numerical integration by the matrix method and evaluation of the approximation order of difference boundary value problems for non-homogeneous linear ordinary differential equations of the fourth order with variable coefficients

Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki, 2020
The use of the second degree Taylor polynomial in approximation of derivatives by finite difference method leads to the second order approximation of the traditional grid method for numerical integration of boundary value problems for non-homogeneous ...
Vladimir Nikolaevich Maklakov, Mariya Aleksandrovna Ilicheva   +1 more
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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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A method for increasing the order of approximation to an arbitrary natural number by the numerical integration of boundary value problems for inhomogeneous linear ordinary differential equations of various degrees with variable coefficients by the matrix method

Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki, 2020
The paper includes the well-known matrix method of numerical integration of boundary value problems for inhomogeneous linear ordinary differential equations with variable coefficients, which provides retaining an arbitrary number of Taylor series ...
Vladimir Nikolaevich Maklakov
doaj   +1 more source

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
doaj   +1 more source

Numerical integration by the matrix method of boundary value problems for linear inhomogeneous ordinary differential equations of the third order with variable coefficients

Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki, 2018
The use of the Taylor polynomial of the second degree when approximating the derivatives by finite differences leads to the second order of approximation of the traditional method of nets in the numerical integration of second-order ordinary differential
Vladimir N Maklakov, Yanina G Stelmakh
doaj   +1 more source

Optimization of the 2P fifth degree convolution kernel in the spectral domain [PDF]

Bulletin of Natural Sciences Research, 2023
The first part of the paper describes a two-parameter (2P) fifth-order interpolation kernel, r. After that, from the 2P kernel, the kernel components were created.
Savić Nataša, Milivojević Zoran, Prlinčević Bojan   +2 more
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Numerical method for a system of integro-differential equations and convergence analysis by Taylor collocation

Ain Shams Engineering Journal, 2018
In this paper, we present the Taylor polynomial solutions of system of higher order linear integro-differential Volterra-Fredholm equations (IDVFE). This method transforms IDVFE into the matrix equations which correspond to a system of linear algebraic ...
Yousef Jafarzadeh, Bagher Keramati
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Faber polynomial coefficient estimates of bi-univalent functions connected with the $q$-convolution [PDF]

Mathematica Bohemica, 2023
We introduce a new class of bi-univalent functions defined in the open unit disc and connected with a $q$-convolution. We find estimates for the general Taylor-Maclaurin coefficients of the functions in this class by using Faber polynomial expansions and
Sheza M. El-Deeb, Serap Bulut
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Recursion Relations for Chromatic Coefficients for Graphs and Hypergraphs

Discussiones Mathematicae Graph Theory, 2022
We establish a set of recursion relations for the coefficients in the chromatic polynomial of a graph or a hypergraph. As an application we provide a generalization of Whitney’s broken cycle theorem for hypergraphs, as well as deriving an explicit ...
Durhuus Bergfinnur, Lucia Angelo
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