相关论文: Enhanced Approximate Cloaking by SH and FSH Lining
We study the problem of approximation of 2D set of points. Such type of problems always occur in physical experiments, econometrics, data analysis and other areas. The often problems of outliers or spikes usually make researchers to apply…
Nearest neighbor search is fundamental to a wide range of applications. Since the exact nearest neighbor search suffers from the "curse of dimensionality", approximate approaches, such as Locality-Sensitive Hashing (LSH), are widely used to…
Establishing almost sure convergence rates for stochastic approximation and reinforcement learning under Markovian noise is a fundamental theoretical challenge. We make progress towards this challenge for a class of stochastic approximation…
We explain how to use smooth bivariate splines of arbitrary degree to solve the exterior Helmholtz equation based on a Perfectly Matched Layer (PML) technique. In a previous study (cf. [26]), it was shown that bivariate spline functions of…
We propose a novel variant of the Localized Orthogonal Decomposition (LOD) method for time-harmonic scattering problems of Helmholtz type with high wavenumber $\kappa$. On a coarse mesh of width $H$, the proposed method identifies local…
We propose some new mixed finite element methods for the time dependent stochastic Stokes equations with multiplicative noise, which use the Helmholtz decomposition of the driving multiplicative noise. It is known [16] that the pressure…
Strong approximation errors of both finite element semi-discretization and spatio-temporal full discretization are analyzed for the stochastic Allen-Cahn equation driven by additive noise in space dimension $d \leq 3$. The full…
To capture and simulate geometric surface evolutions, one effective approach is based on the phase field methods. Among them, it is important to design and analyze numerical approximations whose error bound depends on the inverse of the…
Similarity search in high-dimensional spaces is an important task for many multimedia applications. Due to the notorious curse of dimensionality, approximate nearest neighbor techniques are preferred over exact searching techniques since…
Lokshtanov et al.~[STOC 2017] introduced \emph{lossy kernelization} as a mathematical framework for quantifying the effectiveness of preprocessing algorithms in preserving approximation ratios. \emph{$\alpha$-approximate reduction rules}…
We study a quantity called discrete layered entropy, which approximates the Shannon entropy within a logarithmic gap. Compared to the Shannon entropy, the discrete layered entropy is piecewise linear, approximates the expected length of the…
We consider the numerical approximation of boundary conditions in radiative transfer problems by a perfectly matched layer approach. The main idea is to extend the computational domain by an absorbing layer and to use an appropriate…
We consider radial complex scaling/perfectly matched layer methods for scalar resonance problems in homogeneous exterior domains. We introduce a new abstract framework to analyze the convergence of domain truncations and discretizations.…
This article deals with the numerical approximation of effective coefficients in stochastic homogenization of discrete linear elliptic equations. The originality of this work is the use of a well-known abstract spectral representation…
Trigonometric polynomials are widely used for the approximation of a smooth function $f$ from a set of nonuniformly spaced samples $\{f(x_j)\}_{j=0}^{N-1}$. If the samples are perturbed by noise, controlling the smoothness of the…
Maximum coverage and minimum set cover problems --collectively called coverage problems-- have been studied extensively in streaming models. However, previous research not only achieve sub-optimal approximation factors and space…
We consider Holder smoothness classes of surfaces for which we construct piecewise polynomial approximation networks, which are graphs with polynomial pieces as nodes and edges between polynomial pieces that are in `good continuation' of…
Numerical homogenization aims to efficiently and accurately approximate the solution space of an elliptic partial differential operator with arbitrarily rough coefficients in a $d$-dimensional domain. The application of the inverse operator…
It is known that a subharmonic function of finite order $\rho$ can be approximated by the logarithm of the modulus of an entire function at the point $z$ outside an exceptional set up to $C\log|z|$. In this article we prove that if such an…
The key challenge in current research into electromagnetic cloaking is to achieve invisibility over an extended bandwidth. There has been significant progress towards this using the idea of cloaking by sweeping under the carpet of Li and…