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
Sign Up to like & getrecommendations! Published in 2018 at "European Journal of Applied Mathematics"
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
An efficient numerical algorithm for solving delay differential equations based on second kind Chebyshev polynomials
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DOI: 10.1063/5.0271644
Abstract: This paper proposes a fast spectral technique based on second kind Chebyshev polynomials (SKCPs) to numerically solve delay differential equations (DDEs). First, we introduce some features of the SKCPs. Then, we use the operational matrices… read more here.
Keywords: differential equations; second kind; chebyshev polynomials; based second ... See more keywords
Tensor Diagrams and Chebyshev Polynomials
Sign Up to like & getrecommendations! Published in 2018 at "International Mathematics Research Notices"
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;
Solution of fractional Sturm–Liouville problems by generalized polynomials
Sign Up to like & getrecommendations! Published in 2024 at "Engineering Computations"
DOI: 10.1108/ec-04-2024-0356
Abstract: PurposeIn this article, we present the numerical solution of fractional Sturm-Liouville problems by using generalized shifted Chebyshev polynomials.Design/methodology/approachWe combine right Caputo and left Riemann–Liouville fractional differential operators for the construction of fractional Sturm–Liouville operators. The… read more here.
Keywords: liouville problems; sturm liouville; fractional sturm; chebyshev polynomials ... See more keywords
Classification of Skin Lesion With Features Extraction Using Quantum Chebyshev Polynomials and Autoencoder From Wavelet-Transformed Images
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DOI: 10.1109/access.2024.3502513
Abstract: Skin, a vital organ acting as a protective barrier to the external environment, plays a pivotal role in overall human health. Early detection of skin diseases is essential, as untreated conditions can escalate to serious… read more here.
Keywords: classification; skin lesion; quantum chebyshev; classification skin ... See more keywords
Distributed Graph Regularized Denoising via Constrained Chebyshev Polynomials
Sign Up to like & getrecommendations! Published in 2024 at "IEEE Signal Processing Letters"
DOI: 10.1109/lsp.2024.3421972
Abstract: The problem of denoising signals, defined over graph domains, using a regularization framework, is considered here. Using the $L^{2}$ norm, the optimum denoising operator involves a matrix inverse. Approximation of the operator via matrix polynomial… read more here.
Keywords: distributed graph; graph regularized; chebyshev polynomials; denoising via ... See more keywords
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
Sign Up to like & getrecommendations! Published in 2019 at "Mathematical Notes"
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;