Numerical analysis and scientific computing
The Top Open Problems editorial order restricted to Computer Science, followed by cross-listed economics entries. Existing relative order is retained, with provisional placements for new game-learning questions; most entries have no individual difficulty assessment. About rankings
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- CS-68 Unrestricted Linear-Circuit Lower Bound for the Discrete Fourier Transform
- CS-100 10 Lectures and 42 Open Problems — Deterministic Restricted Isometry Property matrices
- CS-101 10 Lectures and 42 Open Problems — Random Partial Discrete Fourier Transform
- CS-258 HHL, Macaulay conditioning, and presentation instability
- CS-277 Nonadaptive Polynomial Stabilization of Minimum-Phase Linear Systems
- CS-278 Stationary and Optimal Linear Differential Behaviors
- CS-301 Achievable External Behaviors Under Controller Interconnection
- CS-304 Global Observability from Negative Gramian Curvature
- CS-317 Polynomial Tractability of Permutation-Invariant Integration
- CS-344 Sampling Complexity of Hyperbolic-Cross Approximation
- CS-346 Practical Sum-of-Squares Tensor Completion
- CS-366 Explicit RIP Matrices Beyond Square-Root Sparsity
- CS-367 Square-Root Sparsity for Explicit RIP Matrices
- CS-392 Convergence and Effective Rates of Unwinding Series
- CS-393 Phase Retrieval from Gabor and Wavelet Magnitudes
- CS-409 Norm Estimation from Asymmetric Black-Box Linear Operators
- CS-427 Moment-SOS Convergence for PDE-Constrained Variational Problems
- CS-429 Adjoint-Free Approximation of Nonsymmetric Low-Rank Matrices
- CS-457 10 Lectures and 42 Open Problems — Certifying the Restricted Isometry Property
- CS-463 Exact ridge reduction for Lévy PIDEs
- CS-467 Exact support and trace-controlled ellipsoidal reachability
- CS-468 From an approximate HJB value to implemented control
- CS-469 Certified weak-coupling tubes for structured reachability
- CS-470 Finite-switch implementation of chattering controls
- CS-471 An intrinsic-dimension certificate for projected Hamilton--Jacobi equations
- CS-628 Fourier Reconstruction of Discrete Objects
- CS-633 Intrinsic Nonlinear Model Reduction
- CS-634 Interpolation-Point Selection in Rational Krylov Reduction
- CS-635 Observability for Polynomial Systems
- CS-636 Threshold-Avoiding Control for Bank Capital Ratios
- CS-637 Redundant Extraction — Bank Capital-Ratio Control
- CS-647 Symmetry-Aware Rank-One Convex Interpolation Algorithms
- CS-659 Reliable Model Reduction for Nonlinear Parameterized Systems
- CS-660 Expansion-Point Selection in Time-Domain Model Reduction
- CS-661 State Recovery from Quantized Nonlinear Trajectories
- CS-664 Explicit Deterministic Restricted Isometry Matrices
- CS-669 Fast Solvers for the Electronic Schrödinger Equation
- CS-670 Low-Rank Subexponential Electronic-Structure Algorithms
- CS-673 Competitiveness of High-Order Hybridizable DG Wave Methods
- CS-691 Numerical Simulation of Dislocation Polygonization
- CS-709 Unified Simplicity Models for Massive Inverse Problems
- CS-720 Automatic Recognition of Numerically Unstable Quadratic Programs
- CS-729 High-Dimensional Regression and PDE Learning Without Dimensional Curse
- CS-750 Condition-Number-Robust Low-Rank Matrix Completion
- CS-752 Optimal Worst-Case Estimators for Signal Reconstruction
- CS-758 Interoperable Virtual Laboratories for Scientific Simulation
- CS-761 Neural Approximation of Strongly Convex Drifts with Linear Error
- CS-778 Sensor-Actuator Co-Design and Distributed Controllability Algorithms
- CS-779 Neural Networks for High-Dimensional Optimal Feedback Control
- CS-804 Improvements to the Signed Heat Method