Given a set T ⊆ GF(q), |T | = t, wT is defined as the smallest positive integer k for which ∑ y∈T y k 6= 0. It can be shown that wT ≤ t always and wT ≤ t − 1 if the characteristic p divides t. T is called a Vandermonde set if wT ≥ t−1 and a super-Vandermonde set if wT = t. This (extremal) algebraic property is interesting for its own right, but the original motivation comes from finite geometri...

We show that the Euclidean condition number of any positive deenite Hankel matrix of order n 3 may be bounded from below by n?1 =(16n) with = exp(4Catalan==) 3:210, and that this bound may be improved at most by a factor 8n. Similar estimates are given for the class of real Vandermonde matrices, the class of row scaled real Vandermonde matrices, and the class of Krylov matrices with Hermitian a...

We consider the problem of interpolating sparse multivariate polynomials from their values. We discuss two algorithms for sparse interpolation, one due to Ben-Or and Tiwari (1988) and the other due to Zippel (1988). We present efficient algorithms for finding the rank of certain special Toeplitz systems arising in the Ben-Or and Tiwari algorithm and for solving transposed Vandermonde systems of...

Al-Saqabi et al. [4] defined a univariate gamma-type function involving the confluent hypergeometirc function of two variables and discussed some associated statistical functions. We define a bivariate extension of their gamma-type function using another form of a confluent hypergeometric function of two variables and discuss some of its statistical functions.

Given a constructor term rewriting system that defines injective functions, the inversion compiler proposed by Nishida, Sakai and Sakabe generates a conditional term rewriting system that defines the inverse relations of the injective functions, and then the compiler unravels the conditional system into an unconditional term rewriting system. In general, the resulting unconditional system is no...

In this note we present a simple proof of a result of Toyama which states that the disjoint union of confluent term rewriting systems is confluent. 1985 Mathematics Subject Classification: 68Q5

A set T ⊂ GF(q), q = ph is a super-Vandermonde set if ∑y∈T yk = 0 for 0 < k < |T |. We determine the structure of super-Vandermonde sets of size p + 1 (almost small) and size q/p − 1 (almost large).

Related DatabasesWeb of Science You must be logged in with an active subscription to view this.Article DataHistorySubmitted: 20 November 2019Accepted: 14 July 2020Published online: 06 May 2021Keywordsinterpolation, least-squares, Vandermonde matrix, Arnoldi, polyval, polyfit, Fourier extensionAMS Subject Headings41A05, 65D05, 65D10Publication DataISSN (print): 0036-1445ISSN (online): 1095-7200P...