Related papers: Convergence analysis of the Generalized Empirical …

When simulating sky images, one often takes a galaxy image $F(x)$ defined by a set of pixelized samples and an interpolation kernel, and then wants to produce a new sampled image representing this galaxy as it would appear with a different…

Constructing or learning a function from a finite number of sampled data points (measurements) is a fundamental problem in science and engineering. This is often formulated as a minimum norm interpolation problem, regularized learning…

In this paper, we study the problem of interpolating a continuous function at $(n+1)$ equally-spaced points in the interval $[0,1]$, using shifts of a kernel on the $(1/n)$-spaced infinite grid. The archetypal example here is approximation…

Kernel interpolation is a fundamental technique for approximating functions from scattered data, with a well-understood convergence theory when interpolating elements of a reproducing kernel Hilbert space. Beyond this classical setting,…

We develop a discrete framework for the interpolation of Banach spaces, which contains the well-known real and complex interpolation methods, but also more recent methods like the Rademacher, $\gamma$- and $\ell^q$-interpolation methods.…

We present a frame interpolation algorithm that synthesizes multiple intermediate frames from two input images with large in-between motion. Recent methods use multiple networks to estimate optical flow or depth and a separate network…

The main aim of this work is to give a general approach to the celebrated Kahane-Salem-Zygmund inequalities. We prove estimates for exponential Orlicz norms of averages $\sup_{1\le j \leq N} \big |\sum_{1 \leq i \leq K}\gamma_i(\cdot)…

We present a novel approach that integrates unfitted finite element methods and neural networks to approximate partial differential equations on complex geometries. Easy-to-generate background meshes (e.g., a simple Cartesian mesh) that cut…

There is an increasing interest in using image-generating diffusion models for deep data augmentation and image morphing. In this context, it is useful to interpolate between latents produced by inverting a set of input images, in order to…

In this paper we present an efficient algorithm for bivariate interpolation, which is based on the use of the partition of unity method for constructing a global interpolant. It is obtained by combining local radial basis function…

Motivated by recent applications of weighted norm inequalities to maximal regularity of first and second order Cauchy problems, we study real interpolation spaces on the basis of general Banach function spaces and, in particular, weighted…

Fast Incremental Expectation Maximization (FIEM) is a version of the EM framework for large datasets. In this paper, we first recast FIEM and other incremental EM type algorithms in the {\em Stochastic Approximation within EM} framework.…

We develop an interpolation-based modeling framework for parameter-dependent partial differential equations arising in control, inverse problems, and uncertainty quantification. The solution is discretized in the physical domain using…

Kernel based regularized interpolation is a well known technique to approximate a continuous multivariate function using a set of scattered data points and the corresponding function evaluations, or data values. This method has some…

In this paper, we propose a new trigonometric interpolation algorithm and establish relevant convergent properties. The method adjusts an existing trigonometric interpolation algorithm such that it can better leverage Fast Fourier Transform…

The main purpose of this paper is to introduce the geometric difference sequence space $l_\infty^{G} (\Delta_G)$ and prove that $l_\infty^{G} ({\Delta}_{G})$ is a Banach space with respect to the norm $\left\|.\right\|^G_{{\Delta}_G}.$ Also…

We provide non asymptotic rates of convergence of the Wasserstein Generative Adversarial networks (WGAN) estimator. We build neural networks classes representing the generators and discriminators which yield a GAN that achieves the minimax…

In this article we develop the Constraint Energy Minimizing Generalized Multiscale Finite Element Method (CEM-GMsFEM) for elliptic partial differential equations with inhomogeneous Dirichlet, Neumann, and Robin boundary conditions, and the…

The main contribution of this paper is twofold: On the one hand, a general framework for performing Hermite interpolation on Riemannian manifolds is presented. The method is applicable, if algorithms for the associated Riemannian…

After a review of the reproducing kernel Banach space framework and semi-inner products, we apply the techniques to the setting of Hardy spaces $H^p$ and Bergman spaces $A^p$, $1<p<\infty$, on the unit ball in $\mathbb{C}^n$, as well as the…