Numerical analysis and scientific computing
Provisional editorial order for Top Open Problems: Millennium Prize Problems first, followed by assessed difficulty tiers; the unassessed remainder keeps its previous catalogue order. About rankings
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- Math-312 Unrestricted Linear-Circuit Lower Bound for the Discrete Fourier Transform
- Math-2068 10 Lectures and 42 Open Problems — Deterministic Restricted Isometry Property matrices
- Math-2069 10 Lectures and 42 Open Problems — Random Partial Discrete Fourier Transform
- Math-4447 HHL, Macaulay conditioning, and presentation instability
- Math-4466 Nonadaptive Polynomial Stabilization of Minimum-Phase Linear Systems
- Math-4467 Stationary and Optimal Linear Differential Behaviors
- Math-4490 Achievable External Behaviors Under Controller Interconnection
- Math-4493 Global Observability from Negative Gramian Curvature
- Math-4506 Polynomial Tractability of Permutation-Invariant Integration
- Math-4533 Sampling Complexity of Hyperbolic-Cross Approximation
- Math-4535 Practical Sum-of-Squares Tensor Completion
- Math-4555 Explicit RIP Matrices Beyond Square-Root Sparsity
- Math-4556 Square-Root Sparsity for Explicit RIP Matrices
- Math-4581 Convergence and Effective Rates of Unwinding Series
- Math-4582 Phase Retrieval from Gabor and Wavelet Magnitudes
- Math-4598 Norm Estimation from Asymmetric Black-Box Linear Operators
- Math-4616 Moment-SOS Convergence for PDE-Constrained Variational Problems
- Math-4618 Adjoint-Free Approximation of Nonsymmetric Low-Rank Matrices
- Math-4992 10 Lectures and 42 Open Problems — Certifying the Restricted Isometry Property
- Math-4998 Exact ridge reduction for Lévy PIDEs
- Math-5002 Exact support and trace-controlled ellipsoidal reachability
- Math-5003 From an approximate HJB value to implemented control
- Math-5004 Certified weak-coupling tubes for structured reachability
- Math-5005 Finite-switch implementation of chattering controls
- Math-5006 An intrinsic-dimension certificate for projected Hamilton--Jacobi equations
- Math-5163 Fourier Reconstruction of Discrete Objects
- Math-5168 Intrinsic Nonlinear Model Reduction
- Math-5169 Interpolation-Point Selection in Rational Krylov Reduction
- Math-5170 Observability for Polynomial Systems
- Math-5171 Threshold-Avoiding Control for Bank Capital Ratios
- Math-5172 Redundant Extraction — Bank Capital-Ratio Control
- Math-5182 Symmetry-Aware Rank-One Convex Interpolation Algorithms
- Math-5194 Reliable Model Reduction for Nonlinear Parameterized Systems
- Math-5195 Expansion-Point Selection in Time-Domain Model Reduction
- Math-5196 State Recovery from Quantized Nonlinear Trajectories
- Math-5199 Explicit Deterministic Restricted Isometry Matrices
- Math-5204 Fast Solvers for the Electronic Schrödinger Equation
- Math-5205 Low-Rank Subexponential Electronic-Structure Algorithms
- Math-5208 Competitiveness of High-Order Hybridizable DG Wave Methods
- Math-5226 Numerical Simulation of Dislocation Polygonization
- Math-5244 Unified Simplicity Models for Massive Inverse Problems
- Math-5255 Automatic Recognition of Numerically Unstable Quadratic Programs
- Math-5264 High-Dimensional Regression and PDE Learning Without Dimensional Curse
- Math-5285 Condition-Number-Robust Low-Rank Matrix Completion
- Math-5287 Optimal Worst-Case Estimators for Signal Reconstruction
- Math-5293 Interoperable Virtual Laboratories for Scientific Simulation
- Math-5296 Neural Approximation of Strongly Convex Drifts with Linear Error
- Math-5313 Sensor-Actuator Co-Design and Distributed Controllability Algorithms
- Math-5314 Neural Networks for High-Dimensional Optimal Feedback Control
- Math-5339 Improvements to the Signed Heat Method