English
Related papers

Related papers: An interpolation problem for functions with values…

200 papers

Interpolation is an essential tool in software verification, where first-order theories are used to constrain datatypes manipulated by programs. In this paper, we introduce the datatype theory of contiguous arrays with maxdiff, where arrays…

Logic in Computer Science · Computer Science 2022-04-26 Silvio Ghilardi , Alessandro Gianola , Deepak Kapur , Chiara Naso

In this work, we study a class of random matrices which interpolate between the Wigner matrix model and various types of patterned random matrices such as random Toeplitz, Hankel, and circulant matrices. The interpolation mechanism is…

Probability · Mathematics 2024-05-14 Frederick Rajasekaran

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

A nonstandard application of bivariate polynomial interpolation is discussed: the implicitization of a rational algebraic curve given by its parametric equations. Three different approaches using the same interpolation space are considered,…

Numerical Analysis · Mathematics 2007-05-23 Ana Marco , Jose-Javier Martinez

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

This paper aims at developing new shape functions adapted to smooth vanishing coefficients for scalar wave equation. It proposes the numerical analysis of their interpolation properties. The interpolation is local but high order convergence…

Numerical Analysis · Mathematics 2019-08-16 Lise-Marie Imbert-Gerard

We reconsider the theory of Lagrange interpolation polynomials with multiple interpolation points and apply it to linear algebra. For instance, $A$ be a linear operator satisfying a degree $n$ polynomial equation $P(A)=0$. One can see that…

Classical Analysis and ODEs · Mathematics 2022-03-04 Askold Khovanskii , Sushil Singla , Aaron Tronsgard

Sampling theory concerns the problem of reconstruction of functions from the knowledge of their values at some discrete set of points. In this paper we derive an orthogonal sampling theory and associated Lagrange interpolation formulae from…

Classical Analysis and ODEs · Mathematics 2015-06-26 Luis O. Silva , Julio H. Toloza

Here the polynomial interpolation approach is used to introduce the main results on multivariate normal algebraic systems. Next we bring a construction which shows that any standard algebraic system, with finite set of solutions, can be…

Numerical Analysis · Mathematics 2025-10-20 H. Hakopian

Given a finite number of samples of a continuous set-valued function F, mapping an interval to compact subsets of the real line, we develop good approximations of F, which can be computed efficiently.

Numerical Analysis · Mathematics 2022-09-01 Qusay Muzaffar , Nira Dyn , David Levin

The usual univariate interpolation problem of finding a monic polynomial f of degree n that interpolates n given values is well understood. This paper studies a variant where f is required to be composite, say, a composition of two…

Algebraic Geometry · Mathematics 2021-03-31 Joachim von zur Gathen , Guillermo Matera

Using polyadic MV algebras, we show that many predicate many valued logics have the interpolation property.

Logic · Mathematics 2013-04-04 Tarek Sayed Ahmed

This paper considers the extension of classical Lagrange interpolation in one real or complex variable to "polynomials of one quaternionic variable". To do this we develop some aspects of the theory of such polynomials. We then give a…

Classical Analysis and ODEs · Mathematics 2020-10-06 Shayne Waldron

Using the theory of representations of the symmetric group, we propose an algorithm to compute the invariant ring of a permutation group. Our approach have the goal to reduce the amount of linear algebra computations and exploit a thinner…

Combinatorics · Mathematics 2015-11-04 Nicolas Borie

Algebraic multigrid (AMG) methods are powerful solvers with linear or near-linear computational complexity for certain classes of linear systems, Ax=b. Broadening the scope of problems that AMG can effectively solve requires the development…

Numerical Analysis · Mathematics 2019-02-15 James Brannick , Scott P. MacLachlan , Jacob B. Schroder , Ben S. Southworth

We consider the problem of identity testing and recovering (that is, interpolating) of a "hidden" monic polynomials $f$, given an oracle access to $f(x)^e$ for $x\in\mathbb F_q$, where $\mathbb F_q$ is the finite field of $q$ elements and…

Computational Complexity · Computer Science 2018-03-02 Marek Karpinski , Laszlo Mérai , Igor E. Shparlinski

In this paper, we consider the structure-preserving model order reduction problem for multi-input/multi-output bilinear control systems by tangential interpolation. We propose a new type of tangential interpolation problem for structured…

Numerical Analysis · Mathematics 2023-11-16 Peter Benner , Serkan Gugercin , Steffen W. R. Werner

Most characterizations of interpolating sequences for Bergman spaces include the condition that the sequence be uniformly discrete in the hyperbolic metric. We show that if the notion of interpolation is suitably generalized, two of these…

Complex Variables · Mathematics 2014-12-03 Daniel H. Luecking

We study continuous homomorphisms between algebras of iterated Laurent series over a commutative ring. We give a full description of such homomorphisms in terms of a discrete data determined by the images of parameters. In similar terms, we…

Rings and Algebras · Mathematics 2016-12-26 Sergey Gorchinskiy , Denis Osipov

The binomial interpolated transform of a sequence is a generalization of the well-known binomial transform. We examine a Pascal-like triangle, on which a binomial interpolated transform works between the left and right diagonals, focusing…

Combinatorics · Mathematics 2021-04-01 László Németh