OOIR: Observatory of International Research

Papers

(The median citation count of Foundations of Computational Mathematics is 2. The table below lists those papers that are above that threshold based on CrossRef citation counts [max. 250 papers]. The publications cover those that have been published in the past four years, i.e., from 2020-04-01 to 2024-04-01.)

Article	Citations
Function Values Are Enough for $$L_2$$-Approximation	28
Error estimates of a Fourier integrator for the cubic Schrödinger equation at low regularity	28
Topological Properties of the Set of Functions Generated by Neural Networks of Fixed Size	27
A Theoretical and Empirical Comparison of Gradient Approximations in Derivative-Free Optimization	27
A Unifying Representer Theorem for Inverse Problems and Machine Learning	26
Complexes from Complexes	19
Kurdyka–Łojasiewicz Exponent via Inf-projection	18
A New Upper Bound for Sampling Numbers	18
Low-Rank Matrix Recovery with Composite Optimization: Good Conditioning and Rapid Convergence	17
Zeroth-Order Nonconvex Stochastic Optimization: Handling Constraints, High Dimensionality, and Saddle Points	17
Primal Dual Methods for Wasserstein Gradient Flows	13
On Randomized Trace Estimates for Indefinite Matrices with an Application to Determinants	13
A Variational Finite Element Discretization of Compressible Flow	13
Sharp Bounds on the Approximation Rates, Metric Entropy, and n-Widths of Shallow Neural Networks	12
A Neural Network-Based Policy Iteration Algorithm with Global $$H^2$$-Superlinear Convergence for Stochastic Games on Domains	12
Newton Polytopes and Relative Entropy Optimization	11
Optimal Stable Nonlinear Approximation	11
An Arbitrary-Order Discrete de Rham Complex on Polyhedral Meshes: Exactness, Poincaré Inequalities, and Consistency	11
Causal Structure Learning: A Combinatorial Perspective	10
Convergence Rates for Discretized Monge–Ampère Equations and Quantitative Stability of Optimal Transport	10
Primary Ideals and Their Differential Equations	10
Convergence Rates of First- and Higher-Order Dynamics for Solving Linear Ill-Posed Problems	9
On the Convergence of Time Splitting Methods for Quantum Dynamics in the Semiclassical Regime	9
A Simple Nearly Optimal Restart Scheme For Speeding Up First-Order Methods	9
Deep Composition of Tensor-Trains Using Squared Inverse Rosenblatt Transports	9

Finite Element Systems for Vector Bundles: Elasticity and Curvature	9
Sparse Harmonic Transforms: A New Class of Sublinear-Time Algorithms for Learning Functions of Many Variables	9
Learning Interaction Kernels in Stochastic Systems of Interacting Particles from Multiple Trajectories	8
A Generalized Conditional Gradient Method for Dynamic Inverse Problems with Optimal Transport Regularization	8
Curve Based Approximation of Measures on Manifolds by Discrepancy Minimization	8
Weak Convergence Rates for Euler-Type Approximations of Semilinear Stochastic Evolution Equations with Nonlinear Diffusion Coefficients	7
Low-Degree Approximation of Random Polynomials	7
Convergence of Adaptive Discontinuous Galerkin and $$C^0$$-Interior Penalty Finite Element Methods for Hamilton–Jacobi–Bellman and Isaacs Equations	7
Wavenumber-Explicit hp-FEM Analysis for Maxwell’s Equations with Transparent Boundary Conditions	7
Fenchel Duality Theory and a Primal-Dual Algorithm on Riemannian Manifolds	7
Analysis of Tensor Approximation Schemes for Continuous Functions	7
Towards Massively Parallel Computations in Algebraic Geometry	7
Do Log Factors Matter? On Optimal Wavelet Approximation and the Foundations of Compressed Sensing	6
Potentially Singular Behavior of the 3D Navier–Stokes Equations	6
A New Technique for Preserving Conservation Laws	6
Euclidean Distance Degree and Mixed Volume	6
Overcoming the Curse of Dimensionality in the Numerical Approximation of Parabolic Partial Differential Equations with Gradient-Dependent Nonlinearities	6
Constraint-Preserving Hybrid Finite Element Methods for Maxwell’s Equations	6
Spectral Graph Matching and Regularized Quadratic Relaxations II	6
Potential Singularity of the 3D Euler Equations in the Interior Domain	6
The Grassmannian of affine subspaces	6
On the Computation of Geometric Features of Spectra of Linear Operators on Hilbert Spaces	6
Computing the Sound of the Sea in a Seashell	6
Homological Algebra for Persistence Modules	6
A Framework for Differential Calculus on Persistence Barcodes	6
Optimality of Robust Online Learning	5
The Saddle Point Problem of Polynomials	5
Orthogonal Polynomials on Planar Cubic Curves	5
Robust Group Synchronization via Cycle-Edge Message Passing	5
Computing the Homology of Semialgebraic Sets. II: General Formulas	5
A Counter-Example to Hausmann’s Conjecture	5
Tensor-Free Proximal Methods for Lifted Bilinear/Quadratic Inverse Problems with Applications to Phase Retrieval	5
Perturbations of Christoffel–Darboux Kernels: Detection of Outliers	5
Order Conditions for Sampling the Invariant Measure of Ergodic Stochastic Differential Equations on Manifolds	5
Sparse Multi-Reference Alignment: Phase Retrieval, Uniform Uncertainty Principles and the Beltway Problem	4
Learning Elliptic Partial Differential Equations with Randomized Linear Algebra	4
Vandermonde Varieties, Mirrored Spaces, and the Cohomology of Symmetric Semi-algebraic Sets	4
Retraction Maps: A Seed of Geometric Integrators	4
Stability of 2-Parameter Persistent Homology	4
Continuum Limit of Lipschitz Learning on Graphs	4
On Numerical Approximations of Fractional and Nonlocal Mean Field Games	4
Efficient and Reliable Algorithms for the Computation of Non-Twist Invariant Circles	4
Metrics, Quantization and Registration in Varifold Spaces	4
A Geometric Integration Approach to Nonsmooth, Nonconvex Optimisation	4
Iterative Potts Minimization for the Recovery of Signals with Discontinuities from Indirect Measurements: The Multivariate Case	4
On the Sample Complexity of Stabilizing Linear Dynamical Systems from Data	4
Covariance’s Loss is Privacy’s Gain: Computationally Efficient, Private and Accurate Synthetic Data	4
Exponential ReLU Neural Network Approximation Rates for Point and Edge Singularities	4
Proximal Methods Avoid Active Strict Saddles of Weakly Convex Functions	4
The Reeb Graph Edit Distance is Universal	4

The Geometry of Off-the-Grid Compressed Sensing	4
Numerical Performance of Optimized Frolov Lattices in Tensor Product Reproducing Kernel Sobolev Spaces	4
Quasi-optimal Nonconforming Approximation of Elliptic PDEs with Contrasted Coefficients and $$H^{1+{r}}$$, $${r}>0$$, Regularity	4
Computing Higher Leray–Serre Spectral Sequences of Towers of Fibrations	4
Affine-Invariant Ensemble Transform Methods for Logistic Regression	3
An Accelerated First-Order Method for Non-convex Optimization on Manifolds	3
Optimization Over the Boolean Hypercube Via Sums of Nonnegative Circuit Polynomials	3
Spectral Graph Matching and Regularized Quadratic Relaxations I Algorithm and Gaussian Analysis	3
Hybrid Transforms of Constructible Functions	3
Stationary Points at Infinity for Analytic Combinatorics	3
Exploiting Sparsity for Semi-Algebraic Set Volume Computation	3
Construction of $$C^2$$ Cubic Splines on Arbitrary Triangulations	3
Drift Estimation of Multiscale Diffusions Based on Filtered Data	3
Analysis and Convergence of Hermite Subdivision Schemes	3
Cumulant–Cumulant Relations in Free Probability Theory from Magnus’ Expansion	3
On the Representation and Learning of Monotone Triangular Transport Maps	3
Mathematics of 2-Dimensional Lattices	3
Noncommutative Polynomials Describing Convex Sets	3
Extremal Points and Sparse Optimization for Generalized Kantorovich–Rubinstein Norms	2
Numerical Accuracy of Ladder Schemes for Parallel Transport on Manifolds	2
A Stirling-Type Formula for the Distribution of the Length of Longest Increasing Subsequences	2
Principal Components Along Quiver Representations	2
Matrix Concentration for Products	2
Most Probable Paths for Anisotropic Brownian Motions on Manifolds	2
Correction To: The Complexity of Factors of Multivariate Polynomials	2
Low-Rank Perturbation of Regular Matrix Pencils with Symmetry Structures	2
Finite Element Approximation of the Levi-Civita Connection and Its Curvature in Two Dimensions	2
Error Analysis for 2D Stochastic Navier–Stokes Equations in Bounded Domains with Dirichlet Data	2
Efficient Computation of the Zeros of the Bargmann Transform Under Additive White Noise	2
Pseudospectral Shattering, the Sign Function, and Diagonalization in Nearly Matrix Multiplication Time	2
Bad and Good News for Strassen’s Laser Method: Border Rank of $$\mathrm{Perm}_3$$ and Strict Submultiplicativity	2
Detection Thresholds in Very Sparse Matrix Completion	2
Functional Equivariance and Conservation Laws in Numerical Integration	2
A Unified Approach to Uniform Signal Recovery From Nonlinear Observations	2
Kähler Geometry of Framed Quiver Moduli and Machine Learning	2
Conormal Spaces and Whitney Stratifications	2
Convergence Analysis under Consistent Error Bounds	2
Approximating Continuous Functions on Persistence Diagrams Using Template Functions	2
Wavenumber-Explicit hp-FEM Analysis for Maxwell’s Equations with Impedance Boundary Conditions	2