Results 31 to 40 of about 1,869 (181)

Brauer-Type Inclusion Sets of Zeros for Chebyshev Polynomial

Mathematics, 2019
The generalized polynomials such as Chebyshev polynomial and Hermite polynomial are widely used in interpolations and numerical fittings and so on. Therefore, it is significant to study inclusion regions of the zeros for generalized polynomials.
Xiao Feng, Yaotang Li
doaj   +1 more source

Asymptotics of Chebyshev polynomials, V. residual polynomials [PDF]

The Ramanujan Journal, 2021
We study residual polynomials, $R_{x_0,n}^{(\mathfrak{e})}$, $\mathfrak{e}\subset\mathbb{R}$, $x_0\in\mathbb{R}\setminus\mathfrak{e}$, which are the degree at most $n$ polynomials with $R(x_0)=1$ that minimize the $\sup$ norm on $\mathfrak{e}$. New are upper bounds on their norms (that are optimal in some cases) and Szegő--Widom asymptotics under ...
Jacob S. Christiansen, Barry Simon, Maxim Zinchenko   +2 more
openaire   +4 more sources

RECURRENCE RELATIONS FOR SOBOLEV ORTHOGONAL POLYNOMIALS

Проблемы анализа, 2020
We consider recurrence relations for the polynomials orthonormal with respect to the Sobolev-type inner product and generated by classical orthogonal polynomials, namely: Jacobi polynomials, Legendre polynomials, Chebyshev polynomials of the first and ...
M. S. Sultanakhmedov
doaj   +1 more source

Some results on complex $(p,q)- $extnsion Chebyshev wavelets [PDF]

Journal of Mahani Mathematical Research
In this paper, we propose a generalized formula for well-known functions such as $(p,q)$-Chebyshev polynomials. Our  consideration is focused on determining properties of generalized Chebyshev polynomials of the first and second kind, sparking interest ...
H. Mazaheri, A.W. Safi, S.M. Jesmani
doaj   +1 more source

Properties of the second-kind Chebyshev polynomials of complex variable

Researches in Mathematics, 2020
We construct a system of functions biorthogonal with Chebyshev polynomials of the second kind on closed contours in the complex plane. Properties of these functions and sufficient conditions of expansion of analytic functions into series in Chebyshev ...
O.V. Veselovska, V.V. Dostoina, M.I. Klapchuk   +2 more
doaj   +1 more source

An approximate solution of the Blasius problem using spectral method

Partial Differential Equations in Applied Mathematics
This paper aims at finding the numerical approximation of a classical Blasius flat plate problem using spectral collocation method. This technique is based on Chebyshev pseudospectral approach that involves the solution is approximated using Chebyshev ...
Zunera Shoukat, Azad Akhter Siddiqui, M. Huzaifa Yaseen, M. Ijaz Khan, Barno Sayfutdinovna Abdullaeva, M. Waqas, Manish Gupta   +6 more
doaj   +1 more source

On the Polynomial Multiplication in Chebyshev Form

IEEE Transactions on Computers, 2012
We give an efficient multiplication method for polynomials in Chebyshev form. This multiplication method is different from the previous ones. Theoretically, we show that the number of multiplications is at least as good as Karatsuba-based algorithm. Moreover, using the proposed method, we improve the number of additions slightly.
Sedat Akleylek, Murat Cenk, Ferruh Özbudak   +2 more
openaire   +3 more sources

Incomplete q-Chebyshev polynomials

Filomat, 2018
In this paper, we get the generating functions of the q-Chebyshev polynomials using ?z operator, which is ?z (f(z))= f(qz) for any given function f (z). Also considering explicit formulas of the q-Chebyshev polynomials, we give new generalizations of the q-Chebyshev polynomials called the incomplete q-Chebyshev polynomials of the first and ...
Cetin, Mirac, Ercan, Elif, TUĞLU, NAİM
openaire   +4 more sources

Machine Learning Interatomic Potentials for Energy Materials: Architectures, Training Strategies, and Applications

Advanced Energy Materials, EarlyView.
Machine learning interatomic potentials bridge quantum accuracy and computational efficiency for materials discovery. Architectures from Gaussian process regression to equivariant graph neural networks, training strategies including active learning and foundation models, and applications in solid‐state electrolytes, batteries, electrocatalysts ...
In Kee Park, Saeed Pourasad, Jinhong Mun, Arunkumar Chitteth Rajan, Tae Hyeon Park, Anand Rohit, Mohammad Zafari, Tan‐Lien Pham, Eunjae Jung, Bonseung Koo, Miran Ha, Gi Beom Sim, Hyun Gyu Park, Won Woong Choi, Kwanghyeon Jo, Soohaeng Yoo Willow, David ChangMo Yang, Chang Woo Myung, Geunsik Lee, Kwang S. Kim   +19 more
wiley   +1 more source

Solving Non-Linear Fractional Variational Problems Using Jacobi Polynomials

Mathematics, 2019
The aim of this paper is to solve a class of non-linear fractional variational problems (NLFVPs) using the Ritz method and to perform a comparative study on the choice of different polynomials in the method.
Harendra Singh, Rajesh K. Pandey, Hari Mohan Srivastava   +2 more
doaj   +1 more source