Solving Symmetric Inverse Sturm–Liouville Problem Using Chebyshev Polynomials
Sign Up to like & getrecommendations! Published in 2019 at "Mediterranean Journal of Mathematics"
DOI: 10.1007/s00009-019-1330-1
Abstract: In this study, we consider Sturm–Liouville equation having a symmetric potential function under the separated boundary conditions on a finite interval. Then, we use Chebyshev polynomials of the first kind for calculating the approximate solution… read more here.
Keywords: liouville; liouville problem; sturm liouville; inverse sturm ... See more keywords
Multilayer Perceptron and Chebyshev Polynomials Based Neural Network for Solving Emden–Fowler Type Initial Value Problems
Sign Up to like & getrecommendations! Published in 2020 at "International Journal of Applied and Computational Mathematics"
DOI: 10.1007/s40819-020-00914-2
Abstract: Present study is devoted to solve singular non-linear differential equations and system of singular non-linear differential equations of Emden–Fowler type using the Multilayer perceptron and Chebyshev polynomials based functional link neural network techniques. We are… read more here.
Keywords: polynomials based; network; multilayer perceptron; chebyshev polynomials ... See more keywords
On certain maximal hyperelliptic curves related to Chebyshev polynomials
Sign Up to like & getrecommendations! Published in 2019 at "Journal of Number Theory"
DOI: 10.1016/j.jnt.2019.03.003
Abstract: We study hyperelliptic curves arising from Chebyshev polynomials. The aim of this paper is to characterize the pairs $(q,d)$ such that the hyperelliptic curve $\cC$ over a finite field $\FF_{q^2}$ corresponding to the equation $y^2… read more here.
Keywords: hyperelliptic curves; curves related; related chebyshev; maximal hyperelliptic ... See more keywords
Chaotic backward shift operator on Chebyshev polynomials
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DOI: 10.1017/s0956792518000670
Abstract: We obtain the representation of the backward shift operator on Chebyshev polynomials involving a principal value (PV) integral. Twice the backward shift on the space of square-summable sequences l2 displays chaotic dynamics, thus we provide… read more here.
Keywords: backward shift; shift operator; chebyshev polynomials; operator ... See more keywords
Tensor Diagrams and Chebyshev Polynomials
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DOI: 10.1093/imrn/rny199
Abstract: In this paper, we describe a class of elements in the ring of $\textrm{SL}(V)$-invariant polynomial functions on the space of configurations of vectors and linear forms of a 3D vector space $V.$ These elements are… read more here.
Keywords: diagrams chebyshev; chebyshev polynomials; tensor diagrams;
Straggler-Exploiting Fully Private Distributed Matrix Multiplication With Chebyshev Polynomials
Sign Up to like & getrecommendations! Published in 2023 at "IEEE Transactions on Communications"
DOI: 10.1109/tcomm.2023.3236385
Abstract: In this paper, we consider coded computation for matrix multiplication tasks in distributed computing to mitigate straggler effects. We assume that the stragglers’ computation results can be leveraged at the master by assigning multiple sub-tasks… read more here.
Keywords: fully private; chebyshev polynomials; master; matrix multiplication ... See more keywords
Chebyshev Polynomials and Integer Coefficients
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DOI: 10.1134/s0001434619010322
Abstract: Generalized Chebyshev polynomials are introduced and studied in this paper. They are applied to obtain a lower bound for the sup-norm on the closed interval for nonzero polynomials with integer coefficients of arbitrary degree. read more here.
Keywords: chebyshev polynomials; polynomials integer; integer coefficients;
On the Chebyshev polynomials and some of their new identities
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DOI: 10.1186/s13662-020-02550-y
Abstract: The main purpose of this paper is, using the elementary methods and properties of the power series, to study the computational problem of the convolution sums of Chebyshev polynomials and Fibonacci polynomials and to give… read more here.
Keywords: chebyshev polynomials; new identities; polynomials new;
Sixth-Kind Chebyshev Spectral Approach for Solving Fractional Differential Equations
Sign Up to like & getrecommendations! Published in 2019 at "International Journal of Nonlinear Sciences and Numerical Simulation"
DOI: 10.1515/ijnsns-2018-0118
Abstract: Abstract The basic aim of this paper is to develop new numerical algorithms for solving some linear and nonlinear fractional-order differential equations. We have developed a new type of Chebyshev polynomials, namely, Chebyshev polynomials of… read more here.
Keywords: chebyshev polynomials; differential equations; proposed algorithms; kind chebyshev ... See more keywords
Solution for the System of Lane–Emden Type Equations Using Chebyshev Polynomials
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DOI: 10.3390/math6100181
Abstract: In this paper, we use the collocation method together with Chebyshev polynomials to solve system of Lane–Emden type (SLE) equations. We first transform the given SLE equation to a matrix equation by means of a… read more here.
Keywords: system; chebyshev polynomials; system lane; solution ... See more keywords
New Results of the Fifth-Kind Orthogonal Chebyshev Polynomials
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DOI: 10.3390/sym13122407
Abstract: The principal objective of this article is to develop new formulas of the so-called Chebyshev polynomials of the fifth-kind. Some fundamental properties and relations concerned with these polynomials are proposed. New moments formulas of these… read more here.
Keywords: new results; fifth kind; results fifth; chebyshev polynomials ... See more keywords