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math.NA2026
Manifold Data Imputation
David Levin
We consider the problem of reconstructing missing data on a smooth manifold from incomplete and nonuniform samples. While classical methods for manifold approximation typically ass…
math.NA2026
Understanding and Resolving Singularities in 3D Dirichlet Boundary Problems
David Levin
We introduce a two-phase approximation method designed to resolve singularities in three-dimensional harmonic Dirichlet problems. The approach utilizes the classical Green's functi…
math.NA2024
Constructing Approximations to Bivariate Piecewise-Smooth Functions
David Levin
This paper demonstrates that the space of piecewise smooth functions can be well approximated by the space of functions defined by a set of simple (non-linear) operations on smooth…