English
Related papers

Related papers: Improved interpolation inequalities on the sphere

200 papers

Theory interpolation has found several successful applications in model checking. We present a novel method for computing interpolants for ground formulas in the theory of equality. The method produces interpolants from colored congruence…

Logic in Computer Science · Computer Science 2015-07-01 Alexander Fuchs , Amit Goel , Jim Grundy , Sava Krstić , Cesare Tinelli

The aim of this paper is to prove an improved version of the bounded differences inequality for matrix valued functions, by developing the methods of Mackey et al.: "Matrix Concentration Inequalities via the Method of Exchangeable Pairs".…

Probability · Mathematics 2013-02-20 Daniel Paulin

In the recent paper [8], a new method to compute stable kernel-based interpolants has been presented. This \textit{rescaled interpolation} method combines the standard kernel interpolation with a properly defined rescaling operation, which…

Numerical Analysis · Mathematics 2018-10-31 Stefano De Marchi , Andrea Idda , Gabriele Santin

In this paper a local approximation method on the sphere is presented. As interpolation scheme we consider a partition of unity method, such as the modified spherical Shepard's method, which uses zonal basis functions (ZBFs) plus spherical…

Numerical Analysis · Mathematics 2014-04-08 Alessandra De Rossi

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…

Astrophysics · Physics 2009-11-07 Marco Lombardi

Standard interpolation techniques are implicitly based on the assumption that the signal lies on a homogeneous domain. In this letter, the proposed interpolation method instead exploits prior information about domain inhomogeneity,…

Classical Analysis and ODEs · Mathematics 2017-04-14 Hamid Behjat , Zafer Doğan , Dimitri Van De Ville , Leif Sörnmo

The present work reports a general method for the calculation of t he polarizability of a truncated sphere on a substrate. A multipole ex pansion is used, where the multipoles are not necessarily localized in the center of the sphere but…

Materials Science · Physics 2010-05-05 Ingve Simonsen , Remi Lazzari , Jacques Jupille , Stephane Roux

We develop two new ideas for interpolation on $\mathbb{S}^2$. In this first part, we will introduce a simple interpolation method named \textit{Spherical Interpolation of orDER} $n$ (SIDER-$n$) that gives a $C^{n}$ interpolant given $n \geq…

Numerical Analysis · Mathematics 2022-12-06 Ki Wai Fong , Shingyu Leung

We consider a family of Gagliardo-Nirenberg-Sobolev interpolation inequalities which interpolate between Sobolev's inequality and the logarithmic Sobolev inequality, with optimal constants. The difference of the two terms in the…

Analysis of PDEs · Mathematics 2012-07-12 Jean Dolbeault , Giuseppe Toscani

Context. The emergence of mixed modes during the subgiant phase, whose frequencies are characterized by a fast evolution with age, can potentially enable a precise determination of stellar properties, a key goal for future missions like…

Solar and Stellar Astrophysics · Physics 2025-01-20 Miguel Clara , Margarida S. Cunha , Pedro P. Avelino , Tiago L. Campante , Sébastien Deheuvels , Daniel R. Reese

We propose and study a new quasi-interpolation method on spheres featuring the following two-phase construction and analysis. In Phase I, we analyze and characterize a large family of zonal kernels (e.g., the spherical version of Poisson…

Numerical Analysis · Mathematics 2025-08-27 Zhengjie Sun , Wenwu Gao , Xingping Sun

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…

Complex Variables · Mathematics 2014-11-13 S. G. Merzlyakov , S. V. Popenov

For the quadratic Lagrange interpolation function, an algorithm is proposed to provide explicit and verified bound for the interpolation error constant that appears in the interpolation error estimation. The upper bound for the…

Numerical Analysis · Mathematics 2017-04-27 Xuefeng Liu , Chun'guang You

We develop a new method to obtain symmetrization inequalities of Sobolev type. Our approach leads to new inequalities and considerable simplification in the theory of embeddings of Sobolev spaces based on rearrangement invariant spaces.

Functional Analysis · Mathematics 2007-06-21 Joaquim Martin , Mario Milman , Evgeniy Pustylnik

We consider interpolation inequalities for imbeddings of the $l^2$-sequence spaces over $d$-dimensional lattices into the $l^\infty_0$ spaces written as interpolation inequality between the $l^2$-norm of a sequence and its difference. A…

Analysis of PDEs · Mathematics 2014-07-03 Alexei Ilyin , Ari Laptev , Sergey Zelik

We present a new technique for the interpolation of discretely-sampled non-negat ive scalar fields across regions of missing data. Any set of basis functions can be used, though the method is fastest when they are close to orthogonal. We…

Astrophysics · Physics 2007-05-23 Will Saunders , Bill E. Ballinger

The goal of this paper is to design compact support basis spline functions that best approximate a given filter (e.g., an ideal Lowpass filter). The optimum function is found by minimizing the least square problem ($\ell$2 norm of the…

Multimedia · Computer Science 2015-03-17 Ramtin Madani , Ali Ayremlou , Arash Amini , Farrokh Marvasti

The problem of extrapolation and interpolation of asymptotic series is considered. Several new variants of improving the accuracy of the self-similar approximants are suggested. The methods are illustrated by examples typical of chemical…

Mathematical Physics · Physics 2010-04-08 V. I. Yukalov , E. P. Yukalova , S. Gluzman

This paper considers the problem of assumptions refinement in the context of unrealizable specifications for reactive systems. We propose a new counterstrategy-guided synthesis approach for GR(1) specifications based on Craig's…

Logic in Computer Science · Computer Science 2018-11-01 Davide G. Cavezza , Dalal Alrajeh

We consider the problem of interpolating a function given on scattered points using Hermite-Birkhoff formulas on the sphere and other manifolds. We express each proposed interpolant as a linear combination of basis functions, the…

Numerical Analysis · Mathematics 2016-11-23 Giampietro Allasia , Roberto Cavoretto , Alessandra De Rossi