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pro vyhledávání: '"65D30"'
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
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
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:
Goda, Takashi, Krieg, David
We present a simple universal algorithm for high-dimensional integration which has the optimal error rate (independent of the dimension) in all weighted Korobov classes both in the randomized and the deterministic setting. Our theoretical findings ar
Externí odkaz:
http://arxiv.org/abs/2411.19164
Autor:
Suzuki, Masato, Tanaka, Ken'ichiro
We propose a quadrature-based formula for computing the exponential function of matrices with a non-oscillatory integral on an infinite interval and an oscillatory integral on a finite interval. In the literature, existing quadrature-based formulas a
Externí odkaz:
http://arxiv.org/abs/2411.19086
Autor:
Waldron, Shayne
We give a simple presentation of the six quaternionic equiangular lines in $\mathbb{H}^2$ as an orbit of the primitive quaternionic reflection group of order 720 (which is isomorphic to 2.A_6 the double cover of $A_6)$. Other orbits of this group are
Externí odkaz:
http://arxiv.org/abs/2411.16766
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
Autor:
Zhou, Hao, Dang, Duy-Minh
This paper addresses a significant gap in rigorous numerical treatments for pricing American options under correlated two-asset jump-diffusion models using the viscosity solution approach, with a particular focus on the Merton model. The pricing of t
Externí odkaz:
http://arxiv.org/abs/2410.04745
We construct an interpolatory high-order cubature rule to compute integrals of smooth functions over self-affine sets with respect to an invariant measure. The main difficulty is the computation of the cubature weights, which we characterize algebrai
Externí odkaz:
http://arxiv.org/abs/2410.00637
Autor:
Wu, Bowei
A extension of the Euler-Maclaurin (E-M) formula to near-singular functions is presented. This extension is derived based on earlier generalized E-M formulas for singular functions. The new E-M formulas consists of two components: a ``singular'' comp
Externí odkaz:
http://arxiv.org/abs/2409.19192