Related papers: Second order interlaced polynomial lattice rules f…

This paper uses the Modified Projection Method to examine the errors in solving the boundary integral equation from Laplace equation. The analysis uses weighted norms, and parallel algorithms help solve the independent linear systems. By…

In this paper, we study functional approximations where we choose the so-called radial basis function method and more specifically, quasi-interpolation. From the various available approaches to the latter, we form new quasi-Lagrange…

We give a new characterization of a continuous embedding between two function spaces of type $G\Gamma$. Such spaces are governed by functionals of type \begin{equation*} \|f\|_{G\Gamma(r,q;w,\delta)} := \left(\int_{0}^{L} \left(…

In this paper, we propose a novel algorithm for function approximation in a weighted Korobov space based on shifted rank-1 lattice rules. To mitigate aliasing errors inherent in lattice-based Fourier coefficient estimation, we employ…

Estimating the normalizing constant of an unnormalized probability distribution has important applications in computer science, statistical physics, machine learning, and statistics. In this work, we consider the problem of estimating the…

The study of iterations of functions over a finite field and the corresponding functional graphs is a growing area of research with connections to cryptography. The behaviour of such iterations is frequently approximated by what is know as…

First passage distributions of semi-Markov processes are of interest in fields such as reliability, survival analysis, and many others. The problem of finding or computing first passage distributions is, in general, quite challenging. We…

In this paper, we study the approximation of $d$-dimensional $\rho$-weighted integrals over unbounded domains $\mathbb{R}_+^d$ or $\mathbb{R}^d$ using a special change of variables, so that quasi-Monte Carlo (QMC) or sparse grid rules can…

The theme of the present paper is numerical integration of $C^r$ functions using randomized methods. We consider variance reduction methods that consist in two steps. First the initial interval is partitioned into subintervals and the…

Many Bayesian inference problems involve high-dimensional models where the performance of standard importance sampling (IS) methods often degrades rapidly as the dimensionality increases. Classical analyses of IS typically rely on the…

We study the polynomial approximation problem in $L^2(\mu_1)$ where $\mu_1(dx) = e^{-|x|}/2 dx$. We show that for any absolutely continuous function $f$, $$ \sum_{k=1}^{\infty} \log^2(e+k) \langle f, P_k \rangle^2 \ \leq C \left(…

In this paper, we analyse a method for approximating the distribution function and density of a random variable that depends in a non-trivial way on a possibly high number of independent random variables, each with support on the whole real…

Real-world machine learning applications may require functions that are fast-to-evaluate and interpretable. In particular, guaranteed monotonicity of the learned function can be critical to user trust. We propose meeting these goals for…

In this paper an iterated function system on the space of distribution functions is built. The inverse problem is introduced and studied by convex optimization problems. Some applications of this method to approximation of distribution…

In this paper, we study the approximation problem for functions in the Gaussian-weighted Sobolev space $W^\alpha_p(\mathbb{R}^d, \gamma)$ of mixed smoothness $\alpha \in \mathbb{N}$ with error measured in the Gaussian-weighted space…

In this work, we investigate the inverse problem of recovering a potential coefficient in an elliptic partial differential equation from the observations at deterministic sampling points in the domain subject to random noise. We employ a…

We study integration and $L^2$-approximation of functions of infinitely many variables in the following setting: The underlying function space is the countably infinite tensor product of univariate Hermite spaces and the probability measure…

We consider linear dynamical systems of ordinary differential equations or differential algebraic equations. Physical parameters are substituted by random variables for an uncertainty quantification. We expand the state variables as well as…

This paper studies a new class of integration schemes for the numerical solution of semi-explicit differential-algebraic equations of differentiation index 2 in Hessenberg form. Our schemes provide the flexibility to choose different…

Within the framework of mappings between affine spaces, the notion of $n$-th polarization of a function will lead to an intrinsic characterization of polynomial functions. We prove that the characteristic features of derivations, such as…