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Discrete Helmholtz Decompositions of Piecewise Constant and Piecewise Affine Vector and Tensor Fields Found. Comput. Math. (IF 3.0) Pub Date : 2024-03-01
Abstract Discrete Helmholtz decompositions dissect piecewise polynomial vector fields on simplicial meshes into piecewise gradients and rotations of finite element functions. This paper concisely reviews established results from the literature which all restrict to the lowest-order case of piecewise constants. Its main contribution consists of the generalization of these decompositions to 3D and of
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Polynomial Factorization Over Henselian Fields Found. Comput. Math. (IF 3.0) Pub Date : 2024-02-21 Maria Alberich-Carramiñana, Jordi Guàrdia, Enric Nart, Adrien Poteaux, Joaquim Roé, Martin Weimann
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Discrete Pseudo-differential Operators and Applications to Numerical Schemes Found. Comput. Math. (IF 3.0) Pub Date : 2024-02-15 Erwan Faou, Benoît Grébert
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On the Existence of Monge Maps for the Gromov–Wasserstein Problem Found. Comput. Math. (IF 3.0) Pub Date : 2024-02-15 Théo Dumont, Théo Lacombe, François-Xavier Vialard
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Stable Spectral Methods for Time-Dependent Problems and the Preservation of Structure Found. Comput. Math. (IF 3.0) Pub Date : 2024-02-15 Arieh Iserles
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Strong Norm Error Bounds for Quasilinear Wave Equations Under Weak CFL-Type Conditions Found. Comput. Math. (IF 3.0) Pub Date : 2024-02-13 Benjamin Dörich
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Low-Dimensional Invariant Embeddings for Universal Geometric Learning Found. Comput. Math. (IF 3.0) Pub Date : 2024-02-08 Nadav Dym, Steven J. Gortler
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Analysis of a Modified Regularity-Preserving Euler Scheme for Parabolic Semilinear SPDEs: Total Variation Error Bounds for the Numerical Approximation of the Invariant Distribution Found. Comput. Math. (IF 3.0) Pub Date : 2024-02-08 Charles-Edouard Bréhier
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Phaseless Sampling on Square-Root Lattices Found. Comput. Math. (IF 3.0) Pub Date : 2024-02-08 Philipp Grohs, Lukas Liehr
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Exotic B-Series and S-Series: Algebraic Structures and Order Conditions for Invariant Measure Sampling Found. Comput. Math. (IF 3.0) Pub Date : 2024-01-19 Eugen Bronasco
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Extremal Points and Sparse Optimization for Generalized Kantorovich–Rubinstein Norms Found. Comput. Math. (IF 3.0) Pub Date : 2023-12-11 Marcello Carioni, José A. Iglesias, Daniel Walter
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Computational Complexity of Decomposing a Symmetric Matrix as a Sum of Positive Semidefinite and Diagonal Matrices Found. Comput. Math. (IF 3.0) Pub Date : 2023-12-08 Levent Tunçel, Stephen A. Vavasis, Jingye Xu
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Efficient Random Walks on Riemannian Manifolds Found. Comput. Math. (IF 3.0) Pub Date : 2023-12-01 Simon Schwarz, Michael Herrmann, Anja Sturm, Max Wardetzky
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Fast Optimistic Gradient Descent Ascent (OGDA) Method in Continuous and Discrete Time Found. Comput. Math. (IF 3.0) Pub Date : 2023-11-29 Radu Ioan Boţ, Ernö Robert Csetnek, Dang-Khoa Nguyen
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On the Representation and Learning of Monotone Triangular Transport Maps Found. Comput. Math. (IF 3.0) Pub Date : 2023-11-16 Ricardo Baptista, Youssef Marzouk, Olivier Zahm
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Wavenumber-Explicit hp-FEM Analysis for Maxwell’s Equations with Impedance Boundary Conditions Found. Comput. Math. (IF 3.0) Pub Date : 2023-11-14 J. M. Melenk, S. A. Sauter
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Communication Lower Bounds for Nested Bilinear Algorithms via Rank Expansion of Kronecker Products Found. Comput. Math. (IF 3.0) Pub Date : 2023-11-06 Caleb Ju, Yifan Zhang, Edgar Solomonik
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Error Analysis for 2D Stochastic Navier–Stokes Equations in Bounded Domains with Dirichlet Data Found. Comput. Math. (IF 3.0) Pub Date : 2023-10-26 Dominic Breit, Andreas Prohl
We study a finite-element based space-time discretisation for the 2D stochastic Navier–Stokes equations in a bounded domain supplemented with no-slip boundary conditions. We prove optimal convergence rates in the energy norm with respect to convergence in probability, that is convergence of order (almost) 1/2 in time and 1 in space. This was previously only known in the space-periodic case, where higher
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A Construction of $$C^r$$ Conforming Finite Element Spaces in Any Dimension Found. Comput. Math. (IF 3.0) Pub Date : 2023-10-17 Jun Hu, Ting Lin, Qingyu Wu
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A New Approach to the Analysis of Parametric Finite Element Approximations to Mean Curvature Flow Found. Comput. Math. (IF 3.0) Pub Date : 2023-10-17 Genming Bai, Buyang Li
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From Kernel Methods to Neural Networks: A Unifying Variational Formulation Found. Comput. Math. (IF 3.0) Pub Date : 2023-10-17 Michael Unser
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Approximation of Generating Function Barcode for Hamiltonian Diffeomorphisms Found. Comput. Math. (IF 3.0) Pub Date : 2023-10-17 Pazit Haim-Kislev, Ofir Karin
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Approximation of Deterministic Mean Field Games with Control-Affine Dynamics Found. Comput. Math. (IF 3.0) Pub Date : 2023-10-17 Justina Gianatti, Francisco J. Silva
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How Much Can One Learn a Partial Differential Equation from Its Solution? Found. Comput. Math. (IF 3.0) Pub Date : 2023-10-17 Yuchen He, Hongkai Zhao, Yimin Zhong
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Gaussian Beam Ansatz for Finite Difference Wave Equations Found. Comput. Math. (IF 3.0) Pub Date : 2023-10-17 Umberto Biccari, Enrique Zuazua
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Toward Computational Morse–Floer Homology: Forcing Results for Connecting Orbits by Computing Relative Indices of Critical Points Found. Comput. Math. (IF 3.0) Pub Date : 2023-10-17 Jan Bouwe van den Berg, Marcio Gameiro, Jean-Philippe Lessard, Rob Van der Vorst
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Convex Analysis on Hadamard Spaces and Scaling Problems Found. Comput. Math. (IF 3.0) Pub Date : 2023-10-17 Hiroshi Hirai
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Implicitisation and Parameterisation in Polynomial Functors Found. Comput. Math. (IF 3.0) Pub Date : 2023-08-28 Andreas Blatter, Jan Draisma, Emanuele Ventura
In earlier work, the second author showed that a closed subset of a polynomial functor can always be defined by finitely many polynomial equations. In follow-up work on \({\text {GL}}_\infty \)-varieties, Bik–Draisma–Eggermont–Snowden showed, among other things, that in characteristic zero every such closed subset is the image of a morphism whose domain is the product of a finite-dimensional affine
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Improved Resolution Estimate for the Two-Dimensional Super-Resolution and a New Algorithm for Direction of Arrival Estimation with Uniform Rectangular Array Found. Comput. Math. (IF 3.0) Pub Date : 2023-08-01 Ping Liu, Habib Ammari
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BGG Sequences with Weak Regularity and Applications Found. Comput. Math. (IF 3.0) Pub Date : 2023-07-27 Andreas Čap, Kaibo Hu
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Optimality of Robust Online Learning Found. Comput. Math. (IF 3.0) Pub Date : 2023-07-26 Zheng-Chu Guo, Andreas Christmann, Lei Shi
In this paper, we study an online learning algorithm with a robust loss function \(\mathcal {L}_{\sigma }\) for regression over a reproducing kernel Hilbert space (RKHS). The loss function \(\mathcal {L}_{\sigma }\) involving a scaling parameter \(\sigma >0\) can cover a wide range of commonly used robust losses. The proposed algorithm is then a robust alternative for online least squares regression
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Symmetric Bases for Finite Element Exterior Calculus Spaces Found. Comput. Math. (IF 3.0) Pub Date : 2023-07-25 Yakov Berchenko-Kogan
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Proof of the Theory-to-Practice Gap in Deep Learning via Sampling Complexity bounds for Neural Network Approximation Spaces Found. Comput. Math. (IF 3.0) Pub Date : 2023-07-12 Philipp Grohs, Felix Voigtlaender
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Further $$\exists {\mathbb {R}}$$ -Complete Problems with PSD Matrix Factorizations Found. Comput. Math. (IF 3.0) Pub Date : 2023-06-22 Yaroslav Shitov
Let A be an \(m\times n\) matrix with nonnegative real entries. The psd rank of A is the smallest k for which there exist two families \((P_1,\ldots ,P_m)\) and \((Q_1,\ldots ,Q_n)\) of positive semidefinite Hermitian \(k\times k\) matrices such that \(A(i|j)={\text {tr}}(P_i Q_j)\) for all i, j. Several questions on the algorithmic complexity of related matrix invariants were posed in recent literature:
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High-Order Lohner-Type Algorithm for Rigorous Computation of Poincaré Maps in Systems of Delay Differential Equations with Several Delays Found. Comput. Math. (IF 3.0) Pub Date : 2023-06-09 Robert Szczelina, Piotr Zgliczyński
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Bias in the Representative Volume Element method: Periodize the Ensemble Instead of Its Realizations Found. Comput. Math. (IF 3.0) Pub Date : 2023-05-30 Nicolas Clozeau, Marc Josien, Felix Otto, Qiang Xu
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Multi-index Sequential Monte Carlo Ratio Estimators for Bayesian Inverse problems Found. Comput. Math. (IF 3.0) Pub Date : 2023-05-08 Ajay Jasra, Kody J. H. Law, Neil Walton, Shangda Yang
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Symmetry and Invariant Bases in Finite Element Exterior Calculus Found. Comput. Math. (IF 3.0) Pub Date : 2023-04-27 Martin W. Licht
We study symmetries of bases and spanning sets in finite element exterior calculus, using representation theory. We want to know which vector-valued finite element spaces have bases invariant under permutation of vertex indices. The permutations of vertex indices correspond to the symmetry group of the simplex. That symmetry group is represented on simplicial finite element spaces by the pullback action
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Nodal Auxiliary Space Preconditioning for the Surface de Rham Complex Found. Comput. Math. (IF 3.0) Pub Date : 2023-04-19 Yuwen Li
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A New Approach to Handle Curved Meshes in the Hybrid High-Order Method Found. Comput. Math. (IF 3.0) Pub Date : 2023-04-18 Liam Yemm
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Correction to: Conormal Spaces and Whitney Stratifications Found. Comput. Math. (IF 3.0) Pub Date : 2023-02-01 Martin Helmer, Vidit Nanda
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A Stirling-Type Formula for the Distribution of the Length of Longest Increasing Subsequences Found. Comput. Math. (IF 3.0) Pub Date : 2023-01-26 Folkmar Bornemann
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Optimal Polynomial Meshes Exist on any Multivariate Convex Domain Found. Comput. Math. (IF 3.0) Pub Date : 2023-01-23 Feng Dai, Andriy Prymak
We show that optimal polynomial meshes exist for every convex body in \({\mathbb {R}}^d\), confirming a conjecture by A. Kroó.
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On the Sample Complexity of Stabilizing Linear Dynamical Systems from Data Found. Comput. Math. (IF 3.0) Pub Date : 2023-01-23 Steffen W. R. Werner, Benjamin Peherstorfer
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Subexponential-Time Algorithms for Sparse PCA Found. Comput. Math. (IF 3.0) Pub Date : 2023-01-19 Yunzi Ding, Dmitriy Kunisky, Alexander S. Wein, Afonso S. Bandeira
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Mathematics of 2-Dimensional Lattices Found. Comput. Math. (IF 3.0) Pub Date : 2022-12-07 Vitaliy Kurlin
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On the Computation of Geometric Features of Spectra of Linear Operators on Hilbert Spaces Found. Comput. Math. (IF 3.0) Pub Date : 2022-12-01 Matthew J. Colbrook
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Counting Real Roots in Polynomial-Time via Diophantine Approximation Found. Comput. Math. (IF 3.0) Pub Date : 2022-11-28 J. Maurice Rojas
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Finite Element Approximation of the Levi-Civita Connection and Its Curvature in Two Dimensions Found. Comput. Math. (IF 3.0) Pub Date : 2022-11-28 Yakov Berchenko-Kogan, Evan S. Gawlik
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Hybrid Transforms of Constructible Functions Found. Comput. Math. (IF 3.0) Pub Date : 2022-11-22 Vadim Lebovici
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Scattering and Uniform in Time Error Estimates for Splitting Method in NLS Found. Comput. Math. (IF 3.0) Pub Date : 2022-11-16 Rémi Carles, Chunmei Su
We consider the nonlinear Schrödinger equation with a defocusing nonlinearity which is mass-(super)critical and energy-subcritical. We prove uniform in time error estimates for the Lie–Trotter time splitting discretization. This uniformity in time is obtained thanks to a vectorfield which provides time decay estimates for the exact and numerical solutions. This vectorfield is classical in scattering
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Sharp Bounds on the Approximation Rates, Metric Entropy, and n-Widths of Shallow Neural Networks Found. Comput. Math. (IF 3.0) Pub Date : 2022-11-09 Jonathan W. Siegel, Jinchao Xu
In this article, we study approximation properties of the variation spaces corresponding to shallow neural networks with a variety of activation functions. We introduce two main tools for estimating the metric entropy, approximation rates, and n-widths of these spaces. First, we introduce the notion of a smoothly parameterized dictionary and give upper bounds on the nonlinear approximation rates, metric
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An Echelon Form of Weakly Infeasible Semidefinite Programs and Bad Projections of the psd Cone Found. Comput. Math. (IF 3.0) Pub Date : 2022-11-04 Gábor Pataki, Aleksandr Touzov
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Convergence Analysis under Consistent Error Bounds Found. Comput. Math. (IF 3.0) Pub Date : 2022-10-18 Tianxiang Liu, Bruno F. Lourenço
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Stability of 2-Parameter Persistent Homology Found. Comput. Math. (IF 3.0) Pub Date : 2022-10-17 Andrew J. Blumberg, Michael Lesnick
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Adversarial Manifold Estimation Found. Comput. Math. (IF 3.0) Pub Date : 2022-10-11 Eddie Aamari, Alexander Knop
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Efficient Computation of the Zeros of the Bargmann Transform Under Additive White Noise Found. Comput. Math. (IF 3.0) Pub Date : 2022-09-27 Luis Alberto Escudero, Naomi Feldheim, Günther Koliander, José Luis Romero
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Covariance’s Loss is Privacy’s Gain: Computationally Efficient, Private and Accurate Synthetic Data Found. Comput. Math. (IF 3.0) Pub Date : 2022-09-20 March Boedihardjo, Thomas Strohmer, Roman Vershynin
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The Bubble Transform and the de Rham Complex Found. Comput. Math. (IF 3.0) Pub Date : 2022-09-20 Richard S. Falk, Ragnar Winther
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Functional Equivariance and Conservation Laws in Numerical Integration Found. Comput. Math. (IF 3.0) Pub Date : 2022-09-20 Robert I. McLachlan, Ari Stern