相关论文: The Fekete problem in segmental polynomial interpo…
We discuss the growth of the Lebesgue constants for polynomial interpolation at Fekete points for fixed degree (one) and varying dimension, and underlying set $K\subset \R^d$ a simplex, ball or cube.
We construct approximate Fekete point sets for kernel-based interpolation by maximising the determinant of a kernel Gram matrix obtained via truncation of an orthonormal expansion of the kernel. Uniform error estimates are proved for kernel…
Motivated by polynomial approximations of differential forms, we study analytical and numerical properties of a polynomial interpolation problem that relies on function averages over interval segments. The usage of segment data gives rise…
This paper is concerned with Lagrange interpolation by total degree polynomials in moderate dimensions. In particular, we are interested in characterising the optimal choice of points for the interpolation problem, where we define the…
The maximum volume principle is investigated as a means to solve the following problem: Given a set of arbitrary interpolation nodes, how to choose a set of polynomial basis functions for which the Lagrange interpolation problem is…
We give the connections among the Fekete sets, the zeros of orthogonal polynomials, $1(w)$-normal point systems, and the nodes of a stable and most economical interpolatory process via the Fej\'er contants. Finally the convergence of a…
We survey what is known about Fekete points/optimal designs for a simplex in $\R^d.$ Several new results are included. The notion of Fej\'er exponenet for a set of interpolation points is introduced.
Let L be a positive line bundle over a compact complex projective manifold X and K be a compact subset of X which is regular in a sense of pluripotential theory. A Fekete configuration of order k is a finite subset of K maximizing a…
Only a few numerical methods can treat boundary value problems on polygonal and polyhedral meshes. The BEM-based Finite Element Method is one of the new discretization strategies, which make use of and benefits from the flexibility of these…
Fekete polynomials associate with each prime number $p$ a polynomial with coefficients $-1$ or $1$ except the constant term, which is 0. These coefficients reflect the distribution of quadratic residues modulo $p$. These polynomials were…
Let K be the closure of a bounded open set with smooth boundary in C^n. A Fekete configuration of order p for K is a finite subset of K maximizing the Vandermonde determinant associated with polynomials of degree at most p. A recent theorem…
In computational practice, we often encounter situations where only measurements at equally spaced points are available. Using standard polynomial interpolation in such cases can lead to highly inaccurate results due to numerical…
Weighted Fekete points are defined as those that maximize the weighted version of the Vandermonde determinant over a fixed set. They can also be viewed as the equilibrium distribution of the unit discrete charges in an external…
A pattern of interpolation nodes on the disk is studied, for which the interpolation problem is theoretically unisolvent, and which renders a minimal numerical condition for the collocation matrix when the standard basis of Zernike…
Building on the first two authors' previous results, we prove a general criterion for convergence of (possibly singular) Bergman measures towards equilibrium measures on complex manifolds. The criterion may be formulated in terms of growth…
In this note, we obtain the growth order of Lebesgue constants for Fekete points associated with tensor powers of a positive line bundle. Moreover, by endowing the space of global holomorphic sections with a natural Gaussian probability…
A sequence of point configurations on a compact complex manifold is asymptotically Fekete if it is close to maximizing a sequence of Vandermonde determinants. These Vandermonde determinants are defined by tensor powers of a Hermitian ample…
The convergence rates on polynomial interpolation in most cases are estimated by Lebesgue constants. These estimates may be overestimated for some special points of sets for functions of limited regularities. In this paper, by applying the…
In this work, we address the problem of polynomial interpolation of non-pointwise data. More specifically, we assume that our input information comes from measurements obtained on diffuse compact domains. Although the nodal and the diffused…
We obtain the convergence speed for Fekete points on uniformly polynomially cuspidal compact sets introduced by Pawlucki and Ple\'sniak. This is done by showing that these sets are $(\mathscr{C}^{\alpha}, \mathscr{C}^{\alpha'})$-regular in…