Related papers: Multivariate piecewise linear interpolation of a r…
The paper focuses on the sparse approximation of signals using overcomplete representations, such that it preserves the (prior) structure of multi-dimensional signals. The underlying optimization problem is tackled using a multi-dimensional…
This paper proves joint convergence of the approximation error for several stochastic integrals with respect to local Brownian semimartingales, for nonequidistant and random grids. The conditions needed for convergence are that the Lebesgue…
The I-patch is a multi-sided surface representation, defined as a combination of implicit ribbon and bounding surfaces, whose pairwise intersections determine the natural boundaries of the patch. Our goal is to show how a collection of…
We consider the application of multilevel Monte Carlo methods to steady state Darcy flow in a random porous medium, described mathematically by elliptic partial differential equations with random coefficients. The levels in the multilevel…
Identifying important features linked to a response variable is a fundamental task in various scientific domains. This article explores statistical inference for simulated Markov random fields in high-dimensional settings. We introduce a…
For any stationary $\mZ^d$-Gibbs measure that satisfies strong spatial mixing, we obtain sequences of upper and lower approximations that converge to its entropy. In the case, $d=2$, these approximations are efficient in the sense that the…
Piecewise regression is a versatile approach used in various disciplines to approximate complex functions from limited, potentially noisy data points. In control, piecewise regression is, e.g., used to approximate the optimal control law of…
The aim of the paper is to derive for the negative correlation function with a time parameter an asymptotic disjunction of the numerical generalized least-squares estimator of an unknown constant mean of random field in fact the correct…
A flexible model for non-stationary Gaussian random fields on hypersurfaces is introduced.The class of random fields on curves and surfaces is characterized by an amplitude spectral density of a second order elliptic differential…
This note discusses an interpolation technique for univariate distributions. In other words, the question is how to obtain a good approximation for f(x|a) if a0 < a < a1 is a control variable and f(x|a0) and f(x|a1) are known. The technique…
We propose and study a general quasi-interpolation framework for stochastic function approximation, which stems and draws motivation from convolution-type solutions for certain practical weighted variational problems. We obtain our…
Monte Carlo simulations are performed to determine the critical percolation threshold for interpenetrating square objects in two dimensions and cubic objects in three dimensions. Simulations are performed for two cases: (i) objects whose…
We propose solution of the problem of the mean square optimal estimation of linear functionals which depend on the unobserved values of a continuous time stochastic process with periodically correlated increments based on observations of…
We consider a wide class of semi linear Hamiltonian partial differential equa- tions and their approximation by time splitting methods. We assume that the nonlinearity is polynomial, and that the numerical tra jectory remains at least uni-…
We describe a framework for defining high-order image models that can be used in a variety of applications. The approach involves modeling local patterns in a multiscale representation of an image. Local properties of a coarsened image…
Chebyshev interpolation is a highly effective, intensively studied method and enjoys excellent numerical properties. The interpolation nodes are known beforehand, implementation is straightforward and the method is numerically stable. For…
For large classes of even-dimensional Riemannian manifolds $(M,g)$, we construct and analyze conformally invariant random fields. These centered Gaussian fields $h=h_g$, called co-polyharmonic Gaussian fields, are characterized by their…
We consider the random field M(t)=\sup_{n\geq 1}\big\{-\log A_{n}+X_{n}(t)\big\}\,,\qquad t\in T\, for a set $T\subset \mathbb{R}^{m}$, where $(X_{n})$ is an iid sequence of centered Gaussian random fields on $T$ and $0<A_{1}<A_{2}<\cdots $…
In this paper, we investigate the problem of designing compact support interpolation kernels for a given class of signals. By using calculus of variations, we simplify the optimization problem from an infinite nonlinear problem to a finite…
In this paper we present a locally and dimension-adaptive sparse grid method for interpolation and integration of high-dimensional functions with discontinuities. The proposed algorithm combines the strengths of the generalised sparse grid…