Related papers: Prescription for choosing an interpolating functio…
The method of Fractional Borel Summation is suggested in conjunction with self-similar factor approximants. The method used for extrapolating asymptotic expansions at small variables to large variables, including the variables tending to…
In this paper, we deal with the challenging computational issue of interpolating large data sets, with eventually non-homogeneous densities. To such scope, the Radial Basis Function Partition of Unity (RBF-PU) method has been proved to be a…
Radio interferometry is an observational technique used to study astrophysical phenomena. Data gathered by an interferometer requires substantial processing before astronomers can extract the scientific information from it. Data processing…
We investigate the construction of approximated exchange-correlation functionals by interpolating locally along the adiabatic connection between the weak- and the strong-coupling regimes, focussing on the effect of using approximate…
We provide a description of the interpolating and sampling sequences on a space of holomorphic functions with a uniform growth restriction defined on finite Riemann surfaces.
In this paper we consider the approximation of functions by radial basis function interpolants. There is a plethora of results about the asymptotic behaviour of the error between appropriately smooth functions and their interpolants, as the…
Designing and implementing systems as an interconnection of smaller subsystems is a common practice for modularity and standardization of components and design algorithms. Although not typically cast in this framework, many of these…
Functional data analysis (FDA) methods have computational and theoretical appeals for some high dimensional data, but lack the scalability to modern large sample datasets. To tackle the challenge, we develop randomized algorithms for two…
The Piecewise Polynomial Interpolation (PPI) function approach is aimed at solving nonlinear programming problems with disjoint feasible regions. In such problems, disjointedness is generally associated with prohibited operating zones,…
Histopolation, or interpolation on segments, is a mathematical technique used to approximate a function $f$ over a given interval $I=[a,b]$ by exploiting integral information over a set of subintervals of $I$. Unlike classical polynomial…
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…
This work is devoted to the study of integration with respect to binomial measures. We develop interpolatory quadrature rules and study their properties. Local error estimates for these rules are derived in a general framework.
A C++ software design is presented that can be used to interpolate data in any number of dimensions. The design is based on a combination of templates of functional collections of elements and so-called type lists. The design allows for…
We develop heuristic interpolation methods for the functions $t \mapsto \log \det \left( \mathbf{A} + t \mathbf{B} \right)$ and $t \mapsto \operatorname{trace}\left( (\mathbf{A} + t \mathbf{B})^{p} \right)$ where the matrices $\mathbf{A}$…
Matrix functions are a central topic of linear algebra, and problems requiring their numerical approximation appear increasingly often in scientific computing. We review various limited-memory methods for the approximation of the action of…
In this paper, we propose a new trigonometric interpolation algorithm and establish relevant convergent properties. The method adjusts an existing trigonometric interpolation algorithm such that it can better leverage Fast Fourier Transform…
The techniques for polynomial interpolation and Gaussian quadrature are generalized to matrix-valued functions. It is shown how the zeros and rootvectors of matrix orthonormal polynomials can be used to get a quadrature formula with the…
Time delay estimation has long been an active area of research. In this work, we show that compressive sensing with interpolation may be used to achieve good estimation precision while lowering the sampling frequency. We propose an…
We consider the problem of obtaining interpolation constraints for function classes, i.e., necessary and sufficient constraints that a set of points, function values and (sub)gradients must satisfy to ensure the existence of a global…
A formulation of variational principles in terms of functional integrals is proposed for any type of local plastic potentials. The minimization problem is reduced to the computation of a path integral. This integral can be used as a…