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## Foundations of Computational Mathematics OnlineFirst articles

08-08-2019

### Second-Order Models for Optimal Transport and Cubic Splines on the Wasserstein Space

On the space of probability densities, we extend the Wasserstein geodesics to the case of higher-order interpolation such as cubic spline interpolation. After presenting the natural extension of cubic splines to the Wasserstein space, we propose a …

05-08-2019

### On the Sample Complexity of the Linear Quadratic Regulator

This paper addresses the optimal control problem known as the linear quadratic regulator in the case when the dynamics are unknown. We propose a multistage procedure, called Coarse-ID control, that estimates a model from a few experimental trials …

05-08-2019

### Mean Estimation and Regression Under Heavy-Tailed Distributions: A Survey

We survey some of the recent advances in mean estimation and regression function estimation. In particular, we describe sub-Gaussian mean estimators for possibly heavy-tailed data in both the univariate and multivariate settings. We focus on …

05-08-2019 Open Access

### Lie–Poisson Methods for Isospectral Flows

The theory of isospectral flows comprises a large class of continuous dynamical systems, particularly integrable systems and Lie–Poisson systems. Their discretization is a classical problem in numerical analysis. Preserving the spectrum in the …

05-08-2019 Open Access

### Computing Tropical Varieties Over Fields with Valuation

We show how the tropical variety of an ideal $$I\unlhd K[x_1,\ldots ,x_n]$$ I ⊴ K [ x 1 , … , x n ] over a field K with non-trivial discrete valuation can always be traced back to the tropical variety of an ideal \pi ^{-1}I\unlhd R\llbracket …