Uniform approximation on a real-analytic manifold

Holomorphic Approximation on Real Submanifolds of a Complex Manifold

Let X be a complex manifold, let 0 be the sheaf of germs of holomorphic functions on X, and let T(K, 0) denote the ring of sections over KQX (holomorphic functions on K, see [5] as a general reference for the terminology used here). If K is a compact set in X, let C(K) be the Banach algebra of continuous complex-valued functions on K with respect to the maximum norm on K. Let A (K) denote the c...

UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction

UMAP (Uniform Manifold Approximation and Projection) is a novel manifold learning technique for dimension reduction. UMAP is constructed from a theoretical framework based in Riemannian geometry and algebraic topology. Œe result is a practical scalable algorithm that applies to real world data. Œe UMAP algorithm is competitive with t-SNE for visualization quality, and arguably preserves more of...

On Constrained Uniform Approximation

A uniform approximation method to solve absolute value equation

In this paper, we propose a parametric uniform approximation method to solve NP-hard absolute value equations. For this, we uniformly approximate absolute value in such a way that the nonsmooth absolute value equation can be formulated as a smooth nonlinear equation. By solving the parametric smooth nonlinear equation using Newton method, for a decreasing sequence of parameters, we can get the ...

Holomorphic Approximation on Totally Real Sub- Manifolds of a Complex Manifold