Related papers: Multivariate Rational Approximation via Low-Rank T…

In this article a fast and parallelizable algorithm for rational approximation is presented. The method, called (P)QR-AAA, is a (parallel) set-valued variant of the AAA algorithm for scalar functions. It builds on the set-valued AAA…

Rational approximation appears in many contexts throughout science and engineering, playing a central role in linear systems theory, special function approximation, and many others. There are many existing methods for solving the rational…

Modern parabolic equation (PE) methods for wave propagation rely on application of a variety of fractional-powered differential operators. Rational approximations of these operators need to properly map their spectra onto the complex plane,…

We provide rigorous theoretical bounds for Anderson acceleration (AA) that allow for approximate calculations when applied to solve linear problems. We show that, when the approximate calculations satisfy the provided error bounds, the…

In this paper, we introduce a method for multivariate function approximation using function evaluations, Chebyshev polynomials, and tensor-based compression techniques via the Tucker format. We develop novel randomized techniques to…

Parameter-dependent models arise in many contexts such as uncertainty quantification, sensitivity analysis, inverse problems or optimization. Parametric or uncertainty analyses usually require the evaluation of an output of a model for many…

An automated resource analysis technique is introduced, targeting a Call-By-Push-Value abstract machine, with memory prediction as a practical goal. The machine has a polymorphic and linear type system enhanced with a first-order logical…

AAA rational approximation has normally been carried out on a discrete set, typically hundreds or thousands of points in a real interval or complex domain. Here we introduce a continuum AAA algorithm that discretizes a domain adaptively as…

In this work, we propose an extensive numerical study on approximating the absolute value function. The methods presented in this paper compute approximants in the form of rational functions and have been proposed relatively recently, e.g.,…

The state-of-art seismic imaging techniques treat inversion tasks such as FWI and LSRTM as PDE-constrained optimization problems. Due to the large-scale nature, gradient-based optimization algorithms are preferred in practice to update the…

We introduce a theoretical framework for the rational approximation of optical response functions in resonant photonic systems. The framework is based on the AAA algorithm and further allows to solve the underlying nonlinear eigenproblems…

Tensor decompositions play a crucial role in numerous applications related to multi-way data analysis. By employing a Bayesian framework with sparsity-inducing priors, Bayesian Tensor Ring (BTR) factorization offers probabilistic estimates…

The task of approximating a function of d variables from its evaluations at a given number of points is ubiquitous in numerical analysis and engineering applications. When d is large, this task is challenged by the so-called curse of…

Computing the discrete rational minimax approximation in the complex plane is challenging. Apart from Ruttan's sufficient condition, there are few other sufficient conditions for global optimality. The state-of-the-art rational…

Low-rank approximation is a fundamental technique in modern data analysis, widely utilized across various fields such as signal processing, machine learning, and natural language processing. Despite its ubiquity, the mechanics of low-rank…

This paper considers an optimization problem for a dynamical system whose evolution depends on a collection of binary decision variables. We develop scalable approximation algorithms with provable suboptimality bounds to provide…

In many contexts, there is interest in selecting the most important variables from a very large collection, commonly referred to as support recovery or variable, feature or subset selection. There is an enormous literature proposing a rich…

In pursuit of reinforcement learning systems that could train in physical environments, we investigate multi-task approaches as a means to alleviate the need for massive data acquisition. In a tabular scenario where the Q-functions are…

Multivariate function approximation is a fundamental problem in machine learning. Classic multivariate function approximations rely on hand-crafted basis functions (e.g., polynomial basis and Fourier basis), which limits their approximation…

Principal component analysis (PCA) requires the computation of a low-rank approximation to a matrix containing the data being analyzed. In many applications of PCA, the best possible accuracy of any rank-deficient approximation is at most a…