English
Related papers

Related papers: Dynamical sampling, derivatives, and interpolation…

200 papers

In this paper, based on Newton interpolation we have proposed a numerical scheme of predictor-corrector type in order to solve fractional differential equations with the fractional derivative involving the Mittag-Leffler function. We have…

Numerical Analysis · Mathematics 2025-11-05 Sami Aljhani

We characterize interpolating sequences for pairs of reproducing kernels $(s, \ell)$, where $s$ is a complete Pick factor of $\ell.$ This answers a question of Aleman, Hartz, McCarthy and Richter.

Functional Analysis · Mathematics 2022-10-27 Georgios Tsikalas

We give a new probabilistic algorithm for interpolating a "sparse" polynomial f given by a straight-line program. Our algorithm constructs an approximation f* of f, such that their difference probably has at most half the number of terms of…

Symbolic Computation · Computer Science 2014-01-24 Andrew Arnold , Mark Giesbrecht , Daniel S. Roche

We provide an integral representation for the (implied) copulas of dependent random variables in terms of their moment generating functions. The proof uses ideas from Fourier methods for option pricing. This representation can be used for a…

Probability · Mathematics 2014-06-24 Antonis Papapantoleon

We present a new formula for the Hermite multivariate interpolation problem in the framework of the Chung--Yao approach. By using the respective univariate interpolation formula, we obtain a direct and explicit solution to the classical…

Numerical Analysis · Mathematics 2026-02-06 Hakop Hakopian

In this paper we obtain a multivariable commutator lifting inequality, which extends to several variables a recent result of Foias, Frazho, and Kaashoek. The inequality yields a multivariable lifting theorem generalizing the noncommutative…

Functional Analysis · Mathematics 2007-05-23 Gelu Popescu

We introduce interpolation analogues of Schur Q-functions - the multiparameter Schur Q-functions. We obtain for them several results: a combinatorial formula, generating functions for one-row and two-rows functions, vanishing and…

Combinatorics · Mathematics 2007-05-23 Vladimir N. Ivanov

Given a convergent sequence of nodes we present a one-dimensional-holomorphic-function version of the Newton interpolation method of polynomials. It also generalises the Taylor and the Laurent formula. In other words, we present an…

Complex Variables · Mathematics 2012-02-28 Tomasz Sobieszek

To approximate solutions of a linear differential equation, we project, via trigonometric interpolation, its solution space onto a finite-dimensional space of trigonometric polynomials and construct a matrix representation of the…

Numerical Analysis · Mathematics 2011-08-30 Oksana Bihun , Austin Bren , Michael Dyrud , Kristin Heysse

A prescription is presented for the interpolation between multi-dimensional distribution templates based on one or multiple model parameters. The technique uses a linear combination of templates, each created using fixed values of the…

Data Analysis, Statistics and Probability · Physics 2014-10-29 Max Baak , Stefan Gadatsch , Robert Harrington , Wouter Verkerke

We study multiple sampling, interpolation and uniqueness for the classical Fock space in the case of unbounded mul-tiplicities.

Complex Variables · Mathematics 2015-12-23 Alexander Borichev , Andreas Hartmann , Karim Kellay , Xavier Massaneda

Using a lemma of Davis on Gram matrices applied to the classical Orthogonal Polynomials to generate reproducing kernel interpolation over the classical domains for polynomials. These kernels have terms which are exact over the rational…

Numerical Analysis · Mathematics 2024-02-21 John Spitzer

We study sampling and interpolation arrays with multiplicities for the spaces P_k of holomorphic polynomials of degree at most k. We find that the geometric conditions satisfied by these arrays are in accordance with the conditions…

Complex Variables · Mathematics 2026-02-09 Carlos A. Cruz , Xavier Massaneda , Joaquim Ortega-Cerdà

Interferometers play an increasingly important role for spatially resolved observations. If employed at full potential, interferometry can probe an enormous dynamic range in spatial scale. Interpretation of the observed visibilities…

Instrumentation and Methods for Astrophysics · Physics 2015-06-19 C. Brinch , C. P. Dullemond

Nonlinear interpolants have been shown useful for the verification of programs and hybrid systems in contexts of theorem proving, model checking, abstract interpretation, etc. The underlying synthesis problem, however, is challenging and…

Logic in Computer Science · Computer Science 2019-08-29 Mingshuai Chen , Jian Wang , Jie An , Bohua Zhan , Deepak Kapur , Naijun Zhan

In this paper, we propose a trigonometric-interpolation approach for solutions of second order nonlinear ODEs with mixed boundary conditions. The method interpolates secondary derivative $y''$ of a target solution $y$ by a trigonometric…

Numerical Analysis · Mathematics 2025-04-29 Xiaorong Zou

Building on recent advances in studying the co-homological properties of Feynman integrals, we apply intersection theory to the computation of Fourier integrals. We discuss applications pertinent to gravitational bremsstrahlung and deep…

High Energy Physics - Theory · Physics 2024-04-11 Giacomo Brunello , Giulio Crisanti , Mathieu Giroux , Pierpaolo Mastrolia , Sid Smith

We consider the problem of recovering (that is, interpolating) and identity testing of a "hidden" monic polynomial $f$, given an oracle access to $f(x)^e$ for $x\in{\mathbb F_q}$ (extension fields access is not permitted). The naive…

Number Theory · Mathematics 2015-02-25 Gabor Ivanyos , Marek Karpinski , Miklos Santha , Nitin Saxena , Igor Shparlinski

We establish best possible pointwise (up to a constant multiple) estimates for approximation, on a finite interval, by polynomials that satisfy finitely many (Hermite) interpolation conditions, and show that these estimates cannot be…

Classical Analysis and ODEs · Mathematics 2021-01-07 Kirill A. Kopotun , Dany Leviatan , Igor A. Shevchuk

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…

Machine Learning · Statistics 2025-04-09 Samuel G. Fadel , Sebastian Mair , Ricardo da S. Torres , Ulf Brefeld