Related papers: An explicit construction of optimized interpolatio…

This paper is concerned with applications of the theory of approximation and interpolation based on compensated convex transforms developed in [K. Zhang, E. Crooks, A. Orlando, Compensated convexity methods for approximations and…

This is the second lecture note on the error analysis of interpolation on simplicial elements without the shape regularity assumption (the previous one is arXiv:1908.03894). In this manuscript, we explain the error analysis of Lagrange…

Hypersimplices are well-studied objects in combinatorics, optimization, and representation theory. For each hypersimplex, we define a new family of subpolytopes, called r-stable hypersimplices, and show that a well-known regular unimodular…

We present an indirect higher order boundary element method utilising NURBS mappings for exact geometry representation and an interpolation-based fast multipole method for compression and reduction of computational complexity, to counteract…

We propose a numerical strategy to generate the anisotropic meshes and select the appropriate stabilized parameters simultaneously for two dimensional convection-dominated convection-diffusion equations by stabilized continuous linear…

Auto encoding models have been extensively studied in recent years. They provide an efficient framework for sample generation, as well as for analysing feature learning. Furthermore, they are efficient in performing interpolations between…

This paper develops an explicit and implementable framework for constructing spherical designs by lifting point sets from tight fusion frames. By combining existing ingredients, we obtain, in every dimension, explicit spherical $5$-designs…

We present an approach to construct efficient sparse summation-by-parts (SBP) operators on triangles and tetrahedra with a tensor-product structure. The operators are constructed by splitting the simplices into quadrilateral or hexahedral…

Using the LePage representation, a strictly stable random element in a Banach space with $\alpha\in(0,2)$ can be represented as a sum of points of a Poisson process. This point process is union-stable, i.e. the union of its two independent…

We give conditions on the exponent function $p(\cdot)$ that imply the existence of embeddings between grand, small and variable Lebesgue spaces. We construct examples to show that our results are close to optimal. Our work extends recent…

We develop a constructive piecewise polynomial approximation theory in weighted Sobolev spaces with Muckenhoupt weights for any polynomial degree. The main ingredients to derive optimal error estimates for an averaged Taylor polynomial are…

Lebesgue curve is a space-filling curve that fills the unit square through linear interpolation. In this study, we generalise Lebesgue's construction to generate space-filling curves from any given planar substitution satisfying a mild…

In this work we construct subdivision schemes refining general subsets of R^n and study their applications to the approximation of set-valued functions. Differently from previous works on set-valued approximation, our methods are developed…

Meshes composed of well-centered simplices have nice orthogonal dual meshes (the dual Voronoi diagram). This is useful for certain numerical algorithms that prefer such primal-dual mesh pairs. We prove that well-centered meshes also have…

Generative models based on normalizing flows are very successful in modeling complex data distributions using simpler ones. However, straightforward linear interpolations show unexpected side effects, as interpolation paths lie outside the…

We generalize the transfinite triangular interpolant of (Nielson, 1987) in order to generate visually smooth (not necessarily polynomial) local interpolating quasi-optimal triangular spline surfaces. Given as input a triangular mesh stored…

This paper outlines a methodology for constructing a geometrically smooth interpolatory curve in $\mathbb{R}^d$ applicable to oriented and flattenable points with $d\ge 2$. The construction involves four essential components: local…

We present a systematic computational framework for generating positive quadrature rules in multiple dimensions on general geometries. A direct moment-matching formulation that enforces exact integration on polynomial subspaces yields…

The calculation of scattering amplitudes at higher orders in perturbation theory has reached a high degree of maturity. However, their usage to produce physical predictions within Monte Carlo programs is often precluded by the slow…

The smallest possible focus is achieved when the focused wave front is the time reversed copy of the light wave packet emitted from a point in space (S. Quabis et al., Opt. Commun. 179 (2000) 1-7). The best physical implementation of such a…