Zobrazeno 1 - 10
of 422
pro vyhledávání: '"41A55"'
Autor:
Salgado, Abner J., Sawyer, Shane E.
We present a technique for approximating solutions to the spectral fractional Laplacian, which is based on the Caffarelli-Silvestre extension and diagonalization. Our scheme uses the analytic solution to the associated eigenvalue problem in the exten
Externí odkaz:
http://arxiv.org/abs/2409.17388
Autor:
Davydov, Oleg, Esposti, Bruno Degli
We suggest a method for simultaneously generating high order quadrature weights for integrals over Lipschitz domains and their boundaries that requires neither meshing nor moment computation. The weights are determined on pre-defined scattered nodes
Externí odkaz:
http://arxiv.org/abs/2409.03567
We propose and study a new quasi-interpolation method on spheres featuring the following two-phase construction and analysis. In Phase I, we analyze and characterize a large family of zonal kernels (e.g., the spherical version of Poisson kernel, Gaus
Externí odkaz:
http://arxiv.org/abs/2408.14803
Autor:
Lindblad, Ayodeji
A $\textit{spherical $t$-design curve}$ was defined by Ehler and Gr\"{o}chenig to be a continuous, piecewise smooth, closed curve on the sphere with finitely many self-intersections whose associated line integral applied to any polynomial of degree $
Externí odkaz:
http://arxiv.org/abs/2408.04044
Autor:
Zheng, Ruigang, Zhuang, Xiaosheng
In this paper, we prove the existence of a spherical $t$-design formed by adding extra points to an arbitrarily given point set on the sphere and, subsequently, deduce the existence of nested spherical designs. Estimates on the number of required poi
Externí odkaz:
http://arxiv.org/abs/2405.10607
Autor:
Nikolov, Geno, Nikolov, Petar
We study two modifications of the trapezoidal product cubature formulae, approximating double integrals over the square domain $[a,b]^2=[a,b]\times [a,b]$. Our modified cubature formulae use mixed type data: except evaluations of the integrand on the
Externí odkaz:
http://arxiv.org/abs/2404.17796
Given a sequence of Marcinkiewicz-Zygmund inequalities in $L_2$ on a compact space, Gr\"ochenig in \cite{G} discussed weighted least squares approximation and least squares quadrature. Inspired by this work, for all $1\le p\le\infty$, we develop weig
Externí odkaz:
http://arxiv.org/abs/2402.19132
Publikováno v:
SIAM Journal on Numerical Analysis Vol. 62, Iss. 5 (2024)
Numerical integration over the real line for analytic functions is studied. Our main focus is on the sharpness of the error bounds. We first derive two general lower estimates for the worst-case integration error, and then apply these to establish lo
Externí odkaz:
http://arxiv.org/abs/2401.07196
The implicit boundary integral method (IBIM) provides a framework to construct quadrature rules on regular lattices for integrals over irregular domain boundaries. This work provides a systematic error analysis for IBIMs on uniform Cartesian grids fo
Externí odkaz:
http://arxiv.org/abs/2312.07722
Autor:
Van Assche, Walter
The zeros of type II multiple orthogonal polynomials can be used for quadrature formulas that approximate $r$ integrals of the same function $f$ with respect to $r$ measures $\mu_1,\ldots,\mu_r$ in the spirit of Gaussian quadrature. This was first su
Externí odkaz:
http://arxiv.org/abs/2309.11864