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pro vyhledávání: '"Kazashi, Yoshihito"'
We propose a randomized lattice algorithm for approximating multivariate periodic functions over the $d$-dimensional unit cube from the weighted Korobov space with mixed smoothness $\alpha > 1/2$ and product weights $\gamma_1,\gamma_2,\ldots\in [0,1]
Externí odkaz:
http://arxiv.org/abs/2409.18757
Gaussian random fields play an important role in many areas of science and engineering. In practice, they are often simulated by sampling from a high-dimensional multivariate normal distribution, which arises from the discretisation of a suitable pre
Externí odkaz:
http://arxiv.org/abs/2407.12149
Publikováno v:
Mathematics of Computation (2024)
In this paper, we set the mathematical foundations of the Dynamical Low-Rank Approximation (DLRA) method for stochastic differential equations (SDEs). DLRA aims at approximating the solution as a linear combination of a small number of basis vectors
Externí odkaz:
http://arxiv.org/abs/2308.11581
Randomized quadratures for integrating functions in Sobolev spaces of order $\alpha \ge 1$, where the integrability condition is with respect to the Gaussian measure, are considered. In this function space, the optimal rate for the worst-case root-me
Externí odkaz:
http://arxiv.org/abs/2212.11476
The sub-optimality of Gauss--Hermite quadrature and the optimality of the trapezoidal rule are proved in the weighted Sobolev spaces of square integrable functions of order $\alpha$, where the optimality is in the sense of worst-case error. For Gauss
Externí odkaz:
http://arxiv.org/abs/2202.11420
Autor:
Kazashi, Yoshihito, Nobile, Fabio
Publikováno v:
SIAM Journal on Numerical Analysis, Vol. 61, Iss. 2 (2023)
A kernel method for estimating a probability density function (pdf) from an i.i.d. sample drawn from such density is presented. Our estimator is a linear combination of kernel functions, the coefficients of which are determined by a linear equation.
Externí odkaz:
http://arxiv.org/abs/2108.12699
Publikováno v:
Numerische Mathematik, volume 150, pages 33--77 (2022)
This paper deals with the kernel-based approximation of a multivariate periodic function by interpolation at the points of an integration lattice -- a setting that, as pointed out by Zeng, Leung, Hickernell (MCQMC2004, 2006) and Zeng, Kritzer, Hicker
Externí odkaz:
http://arxiv.org/abs/2007.06367
Publikováno v:
Numerische Mathematik volume 149, pages 973--1024 (2021)
We consider the Dynamical Low Rank (DLR) approximation of random parabolic equations and propose a class of fully discrete numerical schemes. Similarly to the continuous DLR approximation, our schemes are shown to satisfy a discrete variational formu
Externí odkaz:
http://arxiv.org/abs/2006.05211
Autor:
Kazashi, Yoshihito, Nobile, Fabio
An existence result is presented for the dynamical low rank (DLR) approximation for random semi-linear evolutionary equations. The DLR solution approximates the true solution at each time instant by a linear combination of products of deterministic a
Externí odkaz:
http://arxiv.org/abs/2002.02356
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