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Foundations of Computational Mathematics

The Journal of the Society for the Foundations of Computational Mathematics

Foundations of Computational Mathematics OnlineFirst articles


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 …


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 …


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 …

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Foundations of Computational Mathematics (FoCM) will publish research and survey papers of the highest quality which further the understanding of the connections between mathematics and computation. The journal aims to promote the exploration of all fundamental issues underlying the creative tension among mathematics, computer science and application areas unencumbered by any external criteria such as the pressure for applications. The journal will thus serve an increasingly important and applicable area of mathematics. The journal hopes to further the understanding of the deep relationships between mathematical theory: analysis, topology, geometry and algebra, and the computational processes as they are evolving in tandem with the modern computer.

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