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pro vyhledávání: '"65D32"'
Nested integration problems arise in various scientific and engineering applications, including Bayesian experimental design, financial risk assessment, and uncertainty quantification. These nested integrals take the form $\int f\left(\int g(\bs{y},\
Externí odkaz:
http://arxiv.org/abs/2412.07723
Autor:
Ali, Ali Hasan, Páles, Zsolt
Publikováno v:
J. Approx. Theory 299 (2024), Paper No. 106019
The aim of this paper is to establish various factorization results and then to derive estimates for linear functionals through the use of a generalized Taylor theorem. Additionally, several error bounds are established including applications to the
Externí odkaz:
http://arxiv.org/abs/2412.05652
We study integration and $L^2$-approximation in the worst-case setting for deterministic linear algorithms based on function evaluations. The underlying function space is a reproducing kernel Hilbert space with a Gaussian kernel of tensor product for
Externí odkaz:
http://arxiv.org/abs/2412.05368
$D$-optimal designs originate in statistics literature as an approach for optimal experimental designs. In numerical analysis points and weights resulting from maximal determinants turned out to be useful for quadrature and interpolation. Also recent
Externí odkaz:
http://arxiv.org/abs/2412.02489
The SE and DE formulas are known as efficient quadrature formulas for integrals with endpoint singularity. Particularly, for integrals with algebraic singularity, explicit error bounds in a computable form have been provided, which are useful for com
Externí odkaz:
http://arxiv.org/abs/2411.19755
Autor:
Wu, Hao-Ning
Given a set of scattered points on a regular or irregular 2D polygon, we aim to employ them as quadrature points to construct a quadrature rule that establishes Marcinkiewicz--Zygmund inequalities on this polygon. The quadrature construction is aided
Externí odkaz:
http://arxiv.org/abs/2411.16584
Utilising classical results on the structure of Hopf algebras, we develop a novel approach for the construction of cubature formulae on Wiener space based on unshuffle expansions. We demonstrate the effectiveness of this approach by constructing the
Externí odkaz:
http://arxiv.org/abs/2411.13707
We develop a recursive integration formula for a class of rational polynomials in 2D. Based on this, we present implementations of finite elements that have rational basis functions. Specifically, we provide simple Matlab implementations of the singu
Externí odkaz:
http://arxiv.org/abs/2411.09485
Many paintings from the 19th century have exhibited signs of fading and discoloration, often linked to cadmium yellow, a pigment widely used by artists during that time. In this work, we develop a mathematical model of the cadmium sulfide photocataly
Externí odkaz:
http://arxiv.org/abs/2411.06997
Autor:
Guth, Philipp A., Kaarnioja, Vesa
There has been a surge of interest in uncertainty quantification for parametric partial differential equations (PDEs) with Gevrey regular inputs. The Gevrey class contains functions that are infinitely smooth with a growth condition on the higher-ord
Externí odkaz:
http://arxiv.org/abs/2411.03793