Related papers: Multivariate Anisotropic Interpolation on the Toru…
Along this work we study an indefinite abstract smoothing problem. After establishing necessary and sufficient conditions for the existence of solutions to this problem, the set of admissible parameters is discussed in detail. Then, its…
We study the supervised clustering problem under the two-component anisotropic Gaussian mixture model in high dimensions and in the non-asymptotic setting. We first derive a lower and a matching upper bound for the minimax risk of…
The dressed states arising from the interaction between electrons and holes, and off-resonant electromagnetic radiation have been investigated for recently fabricated gapped and anisotropic black phosphorus. Our calculations were carried…
Given a function f defined on a bidimensional bounded domain and a positive integer N, we study the properties of the triangulation that minimizes the distance between f and its interpolation on the associated finite element space, over all…
The interaction between two particles with shape or interaction anisotropy can be modeled using a pairwise potential energy function that depends on their relative position and orientation; however, this function is often challenging to…
We study the approximation of maps into complex manifolds along with interpolation on certain compact subsets of the plane. Results are also obtained regarding approximation and interpolation of sections of holomorphic submersions.
Recently, the $\vec{H}(\operatorname{div})$-conforming finite element families for second order elliptic problems have come more into focus, since due to hybridization and subsequent advances in computational efficiency their use is no…
We study in this paper the function approximation error of multivariate linear extrapolation. The sharp error bound of linear interpolation already exists in the literature. However, linear extrapolation is used far more often in…
We study anisotropic undersampling schemes like those used in multi-dimensional NMR spectroscopy and MR imaging, which sample exhaustively in certain time dimensions and randomly in others. Our analysis shows that anisotropic undersampling…
Smoothing is omnipresent in astronomy, because almost always measurements performed at discrete positions in the sky need to be interpolated into a smooth map for subsequent analysis. Still, the statistical properties of different…
The error between appropriately smooth functions and their radial basis function interpolants, as the interpolation points fill out a bounded domain in R^d, is a well studied artifact. In all of these cases, the analysis takes place in a…
This article aims to study fractal interpolation functions corresponding to a sequence of iterated function systems (IFSs). For a suitable choice of a sequence of IFS parameters, the corresponding non-stationary fractal function is a better…
Several inequalities for the isoperimetric ratio for plane curves are derived. In particular, we obtain interpolation inequalities between the deviation of curvature and the isoperimetric ratio. As applications, we study the large-time…
We propose a method to overcome the usual limitation of current data processing techniques in optical and infrared long-baseline interferometry: most reduction pipelines assume uncorrelated statistical errors and ignore systematics. We use…
For pulsar projects it is often necessary to predict the pulse phase in advance, for example, when preparing for new observations. Interpolation of the pulse phase between existing measurements is also often required, for example, when…
Asymmetry measurements are common in collider experiments and can sensitively probe particle properties. Typically, data can only be measured in a finite region covered by the detector, so an extrapolation from the visible asymmetry to the…
We introduce interpolation operators with approximation and stability properties suited for parabolic problems in primal and mixed formulations. We derive localized error estimates for tensor product meshes (occurring in classical…
In [Kopteva, Math. Comp., 2014] a counterexample of an anisotropic triangulation was given on which the exact solution has a second-order error of linear interpolation, while the computed solution obtained using linear finite elements is…
We study the effects of anisotropic pressure on the properties of spherically symmetric, gravitationally bound objects. We consider the full general relativistic treatment of this problem and obtain exact solutions for various form of…
A general theory for obtaining anisotropic interpolation error estimates for macro-element interpolation is developed revealing general construction principles. We apply this theory to interpolation operators on a macro type of biquadratic…