Related papers: Artin approximation compatible with a change of va…
Statistical applications often involve the calculation of intractable multidimensional integrals. The Laplace formula is widely used to approximate such integrals. However, in high-dimensional or small sample size problems, the shape of the…
We construct a Lipschitz truncation which approximates functions of bounded variation in the area-strict metric. The Lipschitz truncation changes the original function only on a small set similar to Lusin's theorem. Previous results could…
Variational methods are employed in situations where exact Bayesian inference becomes intractable due to the difficulty in performing certain integrals. Typically, variational methods postulate a tractable posterior and formulate a lower…
We present a novel artificial diffusion method to circumvent the instabilities associated with the standard finite element approximation of convection-diffusion equations. Motivated by the micromorphic approach, we introduce an auxiliary…
There has been substantial progress on finding game-theoretic equilibria. Most of that work has focused on games with finite, discrete action spaces. However, many games involving space, time, money, and other fine-grained quantities have…
We propose an augmented Lagrangian-type algorithm for the solution of generalized Nash equilibrium problems (GNEPs). Specifically, we discuss the convergence properties with regard to both feasibility and optimality of limit points. This is…
We propose new approximate alternating projection methods, based on randomized sketching, for the low-rank nonnegative matrix approximation problem: find a low-rank approximation of a nonnegative matrix that is nonnegative, but whose…
Gaussian variational approximations are widely used for summarizing posterior distributions in Bayesian models, especially in high-dimensional settings. However, a drawback of such approximations is the inability to capture skewness or more…
A recently developed method has been extended to a nonlocal equation arising in steady water wave propagation in two dimensions. We obtain analyic approximation of steady water wave solution in two dimensions with rigorous error bounds for…
We propose a new adaptive algorithm for the approximation of the Landau-Lifshitz-Gilbert equation via a higher-order tangent plane scheme. We show that the adaptive approximation satisfies an energy inequality and demonstrate numerically,…
In the article we propose a general scheme for solutions of some approximation problems under a rather general setting. We illustrate the application of the proposed scheme by a series of examples, in particular we show that many results in…
We derive sufficient conditions for the existence of the Weber formal solution of the corresponding integral equation, related to the familiar Weber-Orr integral transforms. This gives a solution to the old Weber-Titchmarsh problem (posed…
The focus of this article is the approximation of functions which are analytic on a compact interval except at the endpoints. Typical numerical methods for approximating such functions depend upon the use of particular conformal maps from…
Exactly solving first-order constraints (i.e., first-order formulas over a certain predefined structure) can be a very hard, or even undecidable problem. In continuous structures like the real numbers it is promising to compute approximate…
We consider a stationary process (with either discrete or continuous time) and find an adaptive approximating stationary process combining approximation quality and supplementary good properties that can be interpreted as additional…
An approximation method is presented for probabilistic inference with continuous random variables. These problems can arise in many practical problems, in particular where there are "second order" probabilities. The approximation, based on…
Fictitious play is an algorithm for computing Nash equilibria of matrix games. Recently, machine learning variants of fictitious play have been successfully applied to complicated real-world games. This paper presents a simple modification…
Consider (analytic, resp. algebraic) map-germs, Maps((k^n,o),(k^m,o)). These germs are traditionally studied up to the right, let-right and contact equivalences. Below G is one of these groups. An important tool in this study is the Artin…
We combine the method of exchangeable pairs with Stein's method for functional approximation. As a result, we give a general linearity condition under which an abstract Gaussian approximation theorem for stochastic processes holds. We apply…
The method of self-similar factor approximants is shown to be very convenient for solving different evolution equations and boundary-value problems typical of physical applications. The method is general and simple, being a straightforward…