Computing minimal interpolants in C(R)
نویسندگان
چکیده
We consider the following interpolation problem. Suppose one is given a finite set E ⊂ R, a function f : E → R, and possibly the gradients of f at the points of E as well. We want to interpolate the given information with a function F ∈ C(R) with the minimum possible value of Lip(∇F ). We present practical, efficient algorithms for constructing an F such that Lip(∇F ) is minimal, or for less computational effort, within a small dimensionless constant of being minimal.
منابع مشابه
Computing minimal interpolants in $C^{1, 1}(\mathbb{R}^d)$
We consider the following interpolation problem. Suppose one is given a finite set E ⊂ R, a function f : E → R, and possibly the gradients of f at the points of E. We want to interpolate the given information with a function F ∈ C(R) with the minimum possible value of Lip(∇F ). We present practical, efficient algorithms for constructing an F such that Lip(∇F ) is minimal, or for less computatio...
متن کاملNon-uniform Interpolatory Subdivision Based on Local Interpolants of Minimal Degree
This paper presents new univariate linear non-uniform interpolatory subdivision constructions that yield high smoothness, C and C, and are based on least-degree spline interpolants. This approach is motivated by evidence, partly presented here, that constructions based on high-degree local interpolants fail to yield satisfactory shape, especially for sparse, non-uniform samples. While this impr...
متن کاملVinter: A Vampire-Based Tool for Interpolation
This paper describes the Vinter tool for extracting interpolants from proofs and minimising such interpolants using various measures. Vinter takes an input problem written in either SMT-LIB or TPTP syntax, generates so called local proofs and then uses a technique of playing in the grey areas of proofs to find interpolants minimal with respect to various measures. Proofs are found using either ...
متن کاملQUASI-PERMUTATION REPRESENTATIONS OF SUZtTKI GROUP
By a quasi-permutation matrix we mean a square matrix over the complex field C with non-negative integral trace. Thus every permutation matrix over C is a quasipermutation matrix. For a given finite group G, let p(G) denote the minimal degree of a faithful permutation representation of G (or of a faithful representation of G by permutation matrices), let q(G) denote the minimal degree of a fai...
متن کاملLeveraging Interpolant Strength in Model Checking
Craig interpolation is a well known method of abstraction successfully used in both hardware and software model checking. The logical strength of interpolants can affect the quality of approximations and consequently the performance of the model checkers. Recently, it was observed that for the same resolution proof a complete lattice of interpolants ordered by strength can be derived. Most stat...
متن کامل