Related papers: A linear barycentric rational interpolant on starl…
This work establishes fast rates of convergence for empirical barycenters over a large class of geodesic spaces with curvature bounds in the sense of Alexandrov. More specifically, we show that parametric rates of convergence are achievable…
We develop the convergence theory for a well-known method for the interpolation of functions on the real axis with rational functions. Precise new error estimates for the interpolant are de- rived using existing theory for trigonometric…
Classical approximation bases such as Chebyshev polynomials provide principled and interpretable representations, but their multivariate tensor-product constructions scale exponentially with dimension and impose axis-aligned structure that…
Recent work introduced a unified framework for steerable and directional wavelets in two and three dimensions that ensures many desirable properties, such as a multi-scale structure, fast transforms, and a flexible angular localization. We…
Functional data registration is a critical challenge in modern statistics, essential for separating phase variability from amplitude variability. While derivative-based frameworks offer mathematically elegant solutions, their dependence on…
The $\ell_2-$ and $\ell_1-$regularized modified Lagrange interpolation formulae over $[-1,1]$ are deduced in this paper. This paper mainly analyzes the numerical characteristics of regularized barycentric interpolation formulae, which are…
We extend the univariate Newton interpolation algorithm to arbitrary spatial dimensions and for any choice of downward-closed polynomial space, while preserving its quadratic runtime and linear storage cost. The generalisation supports any…
We introduce an extension of interpolation theory to more than two spaces by employing a functional parameter, while retaining a fully functorial and systematic framework. This approach allows for the construction of generalized…
We give necessary and sufficient conditions for the convergence with geometric rate of the common denominators of simultaneous rational interpolants with a bounded number of poles. The conditions are expressed in terms of intrinsic…
This article pertains to interpolation of Sobolev functions at shrinking lattices $h\mathbb{Z}^d$ from $L_p$ shift-invariant spaces associated with cardinal functions related to general multiquadrics,…
We consider sequences of rational interpolants $r_n(z)$ of degree $n$ to the exponential function $e^z$ associated to a triangular scheme of complex points $\{z_{j}^{(2n)}\}_{j=0}^{2n}$, $n>0$, such that, for all $n$, $|z_{j}^{(2n)}|\leq…
Numerical interpolation techniques are widely employed for calculating large rational functions in scattering amplitude computations. It has been observed in recent years that these rational functions greatly simplify upon partial…
In the space of holomorphic functions in a convex domain it is studied the interpolation problem by means of sums of the series of exponentials converging uniformly on all compact sets of the domain. The discrete set of the interpolation…
Barycentric interpolation is arguably the method of choice for numerical polynomial interpolation. The polynomial interpolant is expressed in terms of function values using the so-called barycentric weights, which depend on the…
This manuscript details the use of the rational Chebyshev transform for describing the transverse dynamics of high-power laser diodes, either broad area lasers, index guided lasers or monolithic master oscillator power amplifier devices.…
A novel basis of discrete analytic polynomials on a rhombic lattice is introduced and the associated convolution product is studied. A class of discrete analytic functions that are rational with respect to this product is also described.
We consider a countably generated and uniformly closed algebra of bounded functions. We assume that there is a lower semicontinuous, with respect to the supremum norm, quadratic form and that normal contractions operate in a certain sense.…
We show that low-rank adaptation of large-scale models suffers from a low stable rank that is well below the linear algebraic rank of the subspace, degrading fine-tuning performance. To mitigate the underutilization of the allocated…
Chebyshev interpolation is a highly effective, intensively studied method and enjoys excellent numerical properties. The interpolation nodes are known beforehand, implementation is straightforward and the method is numerically stable. For…
Using polynomial interpolation, along with structural properties of the family of positive real rational functions, we here show that a set of m nodes in the open left half of the complex plane, can always be mapped to anywhere in the…