Biorthogonality of the Lagrange interpolants

Biorthogonality of the Lagrange interpolants

The Newton-Lagrange interpolation is a well-known problem in elementary calculus. Recall basic facts concerning this problem [6], [2]. Let Ak, k = 0, 1, 2, . . . and ak, k = 0, 1, 2, . . . be two arbitrary sequences of complex numbers (we assume that all ak are distinct ak 6= aj if k 6= j. By interpolation polynomial we mean a n-degree polynomial Pn(z) whose values at points a0, a1, . . . , an ...

On a Conjecture of Carl de Boor Regarding the Limits of Lagrange Interpolants

The purpose of this paper is to provide a counterexample to a conjecture of Carl de Boor [2], that every ideal projector is a limit of Lagrange projectors. The counterexample is based on a construction of A. Iarrobino [9] pointed to in this context by G. Ellingsrud (as mentioned in de Boor’s paper [2]). We also show that the conjecture is true for polynomials in two variables.

Backward Error of Polynomial Eigenvalue Problems Solved by Linearization of Lagrange Interpolants

This article considers the backward error of the solution of polynomial eigenvalue problems expressed as Lagrange interpolants. One of the most common strategies to solve polynomial eigenvalue problems is to linearize, which is to say that the polynomial eigenvalue problem is transformed into an equivalent larger linear eigenvalue problem, and solved using any appropriate eigensolver. Much of t...

Continuous Biorthogonality of the Elliptic Hypergeometric Function

We construct a family of continuous biorthogonal functions related to an elliptic analogue of the Gauss hypergeometric function. The key tools used for that are the elliptic beta integral and the integral Bailey chain introduced earlier by the author. Relations to the Sklyanin algebra and elliptic analogues of the Faddeev modular double are discussed in detail.

Biorthogonality and Integration