Related papers: Rational minimax approximation via adaptive baryce…

Building on the blueprint from Goemans and Williamson (1995) for the Max-Cut problem, we construct a polynomial-time approximation algorithm for orthogonally constrained quadratic optimization problems. First, we derive a semidefinite…

We present new algorithms to compute the mean of a set of empirical probability measures under the optimal transport metric. This mean, known as the Wasserstein barycenter, is the measure that minimizes the sum of its Wasserstein distances…

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…

We propose a computational framework for computing low-rank approximations to the ensemble of solutions of a parametrized system of the form $A(\xi)x(\xi)+g(x(\xi))=b(\xi)$ for multiple parameter values. The central idea is to reinterpret…

Potential theory for rational approximation is reviewed by means of examples computed with the AAA algorithm.

We develop approximation algorithms for set-selection problems with deterministic constraints, but random objective values, i.e., stochastic probing problems. When the goal is to maximize the objective, approximation algorithms for probing…

We propose a numerical algorithm for the computation of multi-marginal optimal transport (MMOT) problems involving general probability measures that are not necessarily discrete. By developing a relaxation scheme in which marginal…

Lawson's iteration is a classical and effective method for solving the linear (polynomial) minimax approximation problem in the complex plane. Extension of Lawson's iteration for the rational minimax approximation problem with both…

Computing Wasserstein barycenters of discrete measures has recently attracted considerable attention due to its wide variety of applications in data science. In general, this problem is NP-hard, calling for practical approximative…

Classically, a mainstream approach for solving a convex-concave min-max problem is to instead solve the variational inequality problem arising from its first-order optimality conditions. Is it possible to solve min-max problems faster by…

Approximate Bayesian computation (ABC) is a family of computational techniques in Bayesian statistics. These techniques allow to fi t a model to data without relying on the computation of the model likelihood. They instead require to…

Approximate Bayesian Computation (ABC) methods are increasingly used for inference in situations in which the likelihood function is either computationally costly or intractable to evaluate. Extensions of the basic ABC rejection algorithm…

We describe a strategy for solving nonlinear eigenproblems numerically. Our approach is based on the approximation of a vector-valued function, defined as solution of a non-homogeneous version of the eigenproblem. This approximation step is…

This paper describes a suite of algorithms for constructing low-rank approximations of an input matrix from a random linear image of the matrix, called a sketch. These methods can preserve structural properties of the input matrix, such as…

Probabilistic variants of Model Order Reduction (MOR) methods have recently emerged for improving stability and computational performance of classical approaches. In this paper, we propose a probabilistic Reduced Basis Method (RBM) for the…

In this paper we consider non-smooth convex optimization problems with (possibly) infinite intersection of constraints. In contrast to the classical approach, where the constraints are usually represented as intersection of simple sets,…

We develop fixed-point algorithms for the approximation of structured matrices with rank penalties. In particular we use these fixed-point algorithms for making approximations by sums of exponentials, or frequency estimation. For the basic…

We introduce a probabilistic approach to the LMS filter. By means of an efficient approximation, this approach provides an adaptable step-size LMS algorithm together with a measure of uncertainty about the estimation. In addition, the…

The low-rank matrix approximation problem is ubiquitous in computational mathematics. Traditionally, this problem is solved in spectral or Frobenius norms, where the accuracy of the approximation is related to the rate of decrease of the…

We develop a general theoretical and algorithmic framework for sparse approximation and structured prediction in $\mathcal{P}_2(\Omega)$ with Wasserstein barycenters. The barycenters are sparse in the sense that they are computed from an…