Zobrazeno 1 - 10
of 525
pro vyhledávání: '"41A50"'
We consider linear second order differential equation y''= f with zero Dirichlet boundary conditions. At the continuous level this problem is solvable using the Green function, and this technique has a counterpart on the discrete level. The discrete
Externí odkaz:
http://arxiv.org/abs/2412.06242
The quasi-2D electrostatic systems, characterized by periodicity in two dimensions with a free third dimension, have garnered significant interest in many fields. We apply the sum-of-Gaussians (SOG) approximation to the Laplace kernel, dividing the i
Externí odkaz:
http://arxiv.org/abs/2412.04595
Autor:
Rubin, Olof
We present a survey of key developments in the study of Chebyshev polynomials, first introduced by P. L. Chebyshev and later significantly expanded upon by G. Faber to the complex setting. Our primary focus is on their defining property: being the po
Externí odkaz:
http://arxiv.org/abs/2411.14175
Autor:
Straton, Jack C.
In a prior paper we found that the Fourier-Legendre series of a Bessel function of the first kind J_{N}\left(kx\right) and of a modified Bessel functions of the first kind I_{N}\left(kx\right) lead to an infinite set of series involving \,_{1}F_{2} h
Externí odkaz:
http://arxiv.org/abs/2412.00019
Publikováno v:
Ukrainskyi Matematychnyi Zhurnal, Vol. 76, no. 7, Aug. 2024, pp. 1007-1023
We established exact in order estimates an approximation of the Sobolev classes $W^{\boldsymbol{r}}_{p,\boldsymbol{\alpha}}(\mathbb{T}^d)$ of periodic functions of many variables with a bounded dominating mixed derivative. The approximation is made u
Externí odkaz:
http://arxiv.org/abs/2410.12448
Autor:
Jawecki, Tobias
In the present work we consider rational best approximations to the exponential function that minimize a uniform error on a subset of the imaginary axis. Namely, Chebyshev approximation and unitary best approximation where the latter is subject to fu
Externí odkaz:
http://arxiv.org/abs/2410.06903
Nowadays, low-rank approximations of matrices are an important component of many methods in science and engineering. Traditionally, low-rank approximations are considered in unitary invariant norms, however, recently element-wise approximations have
Externí odkaz:
http://arxiv.org/abs/2410.05247
Autor:
Jawecki, Tobias
Previous works show convergence of rational Chebyshev approximants to the Pad\'e approximant as the underlying domain of approximation shrinks to the origin. In the present work, the asymptotic error and interpolation properties of rational Chebyshev
Externí odkaz:
http://arxiv.org/abs/2410.04885
Autor:
Christiansen, Jacob S., Rubin, Olof
We investigate Chebyshev polynomials corresponding to Jacobi weights and determine monotonicity properties of their related Widom factors. This complements work by Bernstein from 1930-31 where the asymptotical behavior of the related Chebyshev norms
Externí odkaz:
http://arxiv.org/abs/2409.02623
Autor:
Tran, Hoang Anh, Toh, Kim-Chuan
We introduce a S.O.S hierarchy of lower bounds for a polynomial optimization problem whose constraint is expressed as a matrix polynomial semidefinite condition. Our approach involves utilizing a penalty function framework to directly address the mat
Externí odkaz:
http://arxiv.org/abs/2406.12013