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1525 papers in math.NA · page 8
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Algebraic curves let ML spectra scale to large models
Free Decompression with Algebraic Spectral Curves
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Scheme conserves total energy and enforces pressure equilibrium for real gases
Pressure-equilibrium-preserving and fully conservative discretization of compressible flow equations for real and thermally perfect gases
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Fourier residual networks converge spectrally on discontinuous functions
Fourier Residual Networks Achieve Spectral Accuracy for Discontinuous Functions
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H^{-1} norm recovered from random test function expectations
Random test functions, $H^{-1}$ norm equivalence, and stochastic variational physics-informed neural networks
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Early thrombus shapes virtual DSA views after aneurysm device placement
Device-Induced Thrombus Formation in Cerebral Aneurysms: Linking Patient-Specific Clot Modeling and Functional Occlusion to Virtual Angiographic Assessment
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Sublinear neural networks represent any convex set
Parametrizing Convex Sets Using Sublinear Neural Networks
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Integrator reaches first-order accuracy for rough Schrödinger potentials
Optimal error bounds on the exponential wave integrator for nonlinear Schr\"odinger equations with highly singular potential
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EWI achieves optimal L2 errors for NLSE at singular potential limit
Optimal error bounds on the exponential wave integrator for nonlinear Schr\"odinger equations with highly singular potential
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Lifting collisions to spheres yields stable kinetic solvers
The consecutive lifting-projection flow as an approximation of Boltzmann and Landau flow
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Regularized McKean-Vlasov dynamics scales sampling to 64 CV dimensions
High-Dimensional Enhanced Sampling via Regularized Path-Dependent McKean--Vlasov Dynamics using Tensor Density Approximation
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Newton-Schulz iteration gives quadratic convergence on Stiefel without retractions
A second-order method landing on the Stiefel manifold via Newton$\unicode{x2013}$Schulz iteration
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Abel equation solutions converge to positive plateaus
Asymptotic Plateaus for Generalized Abel Equations with Financial Applications
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Generalized Abel equations admit exact asymptotic plateaus
Asymptotic Plateaus for Generalized Abel Equations with Financial Applications
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Factorization locates biharmonic obstacles from far fields
Factorization and monotonicity methods for reconstructing impenetrable obstacles in inverse biharmonic scattering
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Neural nets capture sharp transitions using geometric mean scale
Two-scale Neural Networks for Singularly Perturbed Dynamical Systems with Multiple Parameters
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Evaporation model fit gives in vivo tear breakup parameters
Parameter estimation for evaporation-driven tear film model in two space dimensions
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Decomposition and lumping speed up random fields on graphs
Efficient generation of Gaussian random fields on metric graphs via domain decomposition and mass matrix lumping
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Few linear contrasts recover exact GP conditionals
Fast and accurate conditioning for large-scale and online Gaussian process prediction problems
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Reformulated fluxes keep shallow-water DG limiting exactly balanced
Well-Balanced Subcell Limiting for Discontinuous Galerkin Discretizations of the Shallow-Water Equations
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LDG schemes retain energy stability for stochastic transport
Structure-preserving LDG methods for linear and nonlinear transport equations with gradient noise
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Finite elements achieve optimal rates for hemivariational inequalities
A Finite Element Method for Elliptic Hemivariational Inequalities in Non-isotropic and Heterogeneous Semipermeable Media
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ZNO uses z-domain poles for stable discrete-time learning
ZNO: Stable Rational Neural Operators in the Z-Domain for Discrete-Time Dynamics
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Fourier network reduces PDE training to one linear solve
Variational Matrix-Learning Fourier Networks for Parametric Multiphysics Surrogates
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Monograph gives explicit Riemannian derivations for matrix-manifold optimization
Foundations of Riemannian Geometry for Riemannian Optimization: A Monograph with Detailed Derivations
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Stagewise rescaling yields almost monotonic energy for MEMS touchdown
A Structure-Preserving Stagewise Rescaling Algorithm for a Two-Dimensional Nonlocal MEMS Equation in an Asymptotically Constant-Feedback Regime
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Local instabilities add only minor controllable error to entropy-stable schemes
On the Practical Impact of Local Linear Instabilities in Entropy-Stable Schemes
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Alternating scheme builds elliptic lower-dimensional quasi-periodic solutions
Numerical Construction of Elliptic Lower-Dimensional Quasi-Periodic Solutions with a Priori Bound
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Mixed FEM for Hall-MHD keeps magnetic field exactly divergence-free
Error analysis of a divergence-preserving mixed finite element scheme for the incompressible Hall--magnetohydrodynamic equations
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Stability estimates proven for nonlocal balance laws with memory
Stability estimates for systems of nonlocal balance laws with memory
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Direct Helmholtz equations solve PEC scattering at every frequency
Maxwell \`a la Helmholtz: Direct boundary integral equations for 3D scattering by perfect electric conductors via Helmholtz operators
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The paper proves existence of optimal solutions for an unregularized optimal control…
Error estimates for an unregularized optimal control problem for the stationary Navier-Stokes equations
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The paper analyzes how the regularity of the integral kernel affects discontinuities in…
Discontinuity Analysis and Semi-Analytic Spectral Approximation for the Nonlocal Poisson Equation
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Low-rank TT format keeps Lindblad evolution CPTP at 10^19 scales
Completely Positive and Trace Preserving Schemes with Tensor Train Compression for the Lindblad Equation
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Quaternion embedding enables nuclear norm for tensor completion
Quaternion Nonlinear Transform-Induced Nuclear Norm for Low-Rank Tensor Completion
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New iterative methods compute quaternion matrix inverses faster
A Family of Iterative Methods for Computing Generalized Inverses of Quaternion Matrices and its Applications
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Neural surrogate speeds heart parameter recovery from ECG
A Neural Latent Dynamics Approach for Solving Inverse Problems in Cardiac Electrophysiology
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SMO for MAPE-loss SVR needs only bound and feasibility changes
Sequential Minimal Optimization for $\varepsilon$-SVR with MAPE Loss and Sample-Dependent Box Constraints
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SMO for MAPE ε-SVR changes only feasibility sets and clipping bounds
Sequential Minimal Optimization for $\varepsilon$-SVR with MAPE Loss and Sample-Dependent Box Constraints
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Spectral interpolation improves accuracy in spherical SISL models
Spectral interpolation in semi-implicit semi-Lagrangian methods for shallow water equations on the sphere
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Nonuniform Alikhanov meshes cut CPU time for nonlinear fractional PDEs
Alikhanov-XfPINNs: Adaptive Physics-Informed Learning for Nonlinear Fractional PDEs on Nonuniform Meshes
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Low-memory short recurrences solve nonsymmetric matrix equations
A class of low-rank short recurrences for nonsymmetric linear matrix equations
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Born series inverts Dirac scattering for waveguide arrays
Inverse Scattering for Dirac Equations Arising in Waveguide Arrays
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Skew Cholesky factorization samples Pfaffian processes exactly
Sampling Pfaffian point processes and the symplectic Arnoldi method
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Graft-host coupling strength sets arrhythmia threshold
Modelling the electrophysiological interactions between human pluripotent cell-derived cardiomyocite grafts and host ventricular tissue
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3R models set sensor needs for Advanced Air Mobility surveillance
Reliability, Robustness, and Resilience Modeling for Surveillance System in Advanced Air Mobility Operations
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Policy learns to compose PDE modules for order-of-magnitude OOD gains
HyCOP: Hybrid Composition Operators for Interpretable Learning of PDEs
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Zeta(3) approximations come from a one-parameter modular form family
Modular Forms and Numerical Explorations of Rational Approximations to $\zeta(3)$
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Tetrahedral subgrids let DG run on any polyhedral mesh
Continuous 3D Finite Element Subgrid Basis Functions for Discontinuous Galerkin Methods on Polyhedral Meshes
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New unmixing metric gives local convergence for nonlinear dictionary signals
Local Geometry of Least Squares for Unmixing Signals with Parameter-Dependent Dictionaries
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MDP value functions are rescaled PageRank vectors on reversed chains
Linking PageRank, Time Reversal, and Policy Evaluation