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pro vyhledávání: '"Serkh, Kirill"'
In this paper we describe an adaptive Levin method for numerically evaluating integrals of the form $\int_\Omega f(\mathbf x) \exp(i g(\mathbf x)) \,d\Omega$ over general domains that have been meshed by transfinite elements. On each element, we appl
Externí odkaz:
http://arxiv.org/abs/2406.14817
Autor:
Patel, Zakaria, Serkh, Kirill
Diffusion models are a powerful class of generative models capable of producing high-quality images from pure noise using a simple text prompt. While most methods which introduce additional spatial constraints into the generated images (e.g., boundin
Externí odkaz:
http://arxiv.org/abs/2405.14101
This paper introduces a new method for the efficient computation of oscillatory multidimensional lattice sums in geometries with boundaries. Such sums are ubiquitous in both pure and applied mathematics, and have immediate applications in condensed m
Externí odkaz:
http://arxiv.org/abs/2403.03213
In theory, diffusion curves promise complex color gradations for infinite-resolution vector graphics. In practice, existing realizations suffer from poor scaling, discretization artifacts, or insufficient support for rich boundary conditions. Previou
Externí odkaz:
http://arxiv.org/abs/2311.14312
Autor:
Zhao, Mohan, Serkh, Kirill
In this paper, we describe an algorithm for approximating functions of the form $f(x) = < \sigma(\mu), x^\mu >$ over $[0,1] \subset \mathbb{R}$, where $\sigma(\mu)$ is some distribution supported on $[a,b]$, with $0
Externí odkaz:
http://arxiv.org/abs/2308.10439
Autor:
Zhao, Mohan, Serkh, Kirill
In this paper, we describe an algorithm for fitting an analytic and bandlimited closed or open curve to interpolate an arbitrary collection of points in $\mathbb{R}^{2}$. The main idea is to smooth the parametrization of the curve by iteratively filt
Externí odkaz:
http://arxiv.org/abs/2301.04241
Autor:
Shen, Zewen, Serkh, Kirill
In this paper, we show that the monomial basis is generally as good as a well-conditioned polynomial basis for interpolation, provided that the condition number of the Vandermonde matrix is smaller than the reciprocal of machine epsilon.
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Externí odkaz:
http://arxiv.org/abs/2212.10519
Autor:
Serkh, Kirill, Bremer, James
It is well known that second order homogeneous linear ordinary differential equations with slowly varying coefficients admit slowly varying phase functions. This observation underlies the Liouville-Green method and many other techniques for the asymp
Externí odkaz:
http://arxiv.org/abs/2211.13744
The Levin method is a well-known technique for evaluating oscillatory integrals, which operates by solving a certain ordinary differential equation in order to construct an antiderivative of the integrand. It was long believed that this approach suff
Externí odkaz:
http://arxiv.org/abs/2211.13400
Autor:
Shen, Zewen, Serkh, Kirill
The accurate and efficient evaluation of Newtonian potentials over general 2-D domains is important for the numerical solution of Poisson's equation and volume integral equations. In this paper, we present a simple and efficient high-order algorithm
Externí odkaz:
http://arxiv.org/abs/2208.10443