Wen-shin Lee* ([email protected]), Mathematics and Computer Science Department, University of Antwerp, Middelheimlaan 1, 2020 Antwerpen, Belgium. Symbolic-Numeric Sparse Polynomial Interpolation. We consider the problem of sparse interpolation of a multivariate polynomial that is given as a black box in floating-point arithmetic. When the target polynomial is sparse, there are efficient inte...

A linear interpolation scheme is termed ‘ideal’ when its errors form a polynomial ideal. The paper surveys basic facts about ideal interpolation and raises some questions. Ideal interpolation is, by definition, given by a linear projector on the space Π of polynomials whose kernel is a polynomial ideal. It is therefore also any linear map, as used in algebra, that associates a polynomial with i...

When passing from one to several variables, the nature and structure of polynomial interpolation changes completely: the solvability of the interpolation problem with respect to a given finite dimensional polynomial space, like all polynomials of at most a certain total degree, depends not only on the number, but significantly on the geometry of the nodes. Thus the construction of interpolation...

We construct Weakly Admissible polynomial Meshes (WAMs) on circular sections, such as symmetric and asymmetric circular sectors, circular segments, zones, lenses and lunes. The construction resorts to recent results on subperiodic trigonometric interpolation. The paper is accompanied by a software package to perform polynomial fitting and interpolation at discrete extremal sets on such regions....

This is a survey of the main results on multivariate polynomial interpolation in the last twenty five years, a period of time when the subject experienced its most rapid development. The problem is considered from two different points of view: the construction of data points which allow unique interpolation for given interpolation spaces as well as the converse. In addition, one section is devo...

The algebraic polynomial interpolation on uniformly distributed nodes is affected by the Runge phenomenon, also when the function to be interpolated is analytic. Among all techniques that have been proposed to defeat this phenomenon, there is the mock-Chebyshev interpolation which is an interpolation made on a subset of the given nodes which elements mimic as well as possible the Chebyshev-Loba...

This text discusses barycentric Lagrange interpolation based on the SIAM REVIEW article of Jean-Paul Berrut and Lloyd N. Trefethen [1]. It also offers additional background information, as well as some MATLAB demonstrations. Interpolation Given a set Dn of n + 1 nodes x j with corresponding values f j where j = 0, . . . ,n, we aim to construct the polynomial that satisfies p(x j) = f j j = 0, ....

The classic polynomial interpolation approach is used to derive a sampling theorem for the class of signals that are the response of systems described by differential equations with constant coefficients. In particular, the polynomial that interpolates the signal between the sampling points for increasing order will give increasing accuracy for stable one-sided sequences, if the sampling rate i...

The interpolation by polynomials or other functions is a rather old method in applied mathematics. In the paper of M. Gasca and T. Sauer [9] it is mentioned that the word ''interpolation'' has apparently been introduced by J.Wallis as early as 1655. Compared to this, polynomial interpolation in several variables is a relatively new topic and it probably only started in the second half of 19 cen...

1 0. PREAMBLE I want to thank the organizers for inviting me to this meeting as it gives me the opportunity to help celebrate Sam Conte who gave me my rst academic job. More than that, he provided my children with many years of summer camp in the wilds of New Hampshire and Wisconsin, and at least two of them think that those summers in New Hampshire were essential for their growing up (and I te...