Pseudo Leja sequences

Abstract

We study pseudo Leja sequences attached to a compact set in the complex plane. The requirements are weaker than those of ordinary Leja sequences, but these sequences still provide excellent points for interpolation of analytic functions and their computation is much easier. We also apply them to the construction of excellent sets of nodes for multivariate interpolation of analytic functions on product sets.

Computing Multivariate Fekete and Leja Points by Numerical Linear Algebra

“…In the case that such points maximize the (absolute value of the) denominator of (4) in K N (Fekete points), then ℓ j ∞ ≤ 1 for every j, and thus the norm of the interpolation operator L S N : C(K) → S N is bounded by the dimension of the interpolation space,…”

“…For an overview about theoretical and computational aspects of Leja points we may quote, e.g., [1,4,5,17,23,28,31] and references therein.…”

Low cardinality admissible meshes on quadrangles, triangles and disks

“…In the complex case, we mention only that it is easy to construct an admissible mesh with O(n) points for any compact set K ⊂ C 1 satisfying a Markov inequality of exponent 1, and boundary given by a C 1 parametric curve, cf. [1,Prop.17].…”

Weakly Admissible Meshes and Discrete Extremal Sets

“…First, we recall that every convex compact set of R 2 with nonempty interior admits the Markov inequality max x∈K ∇p(x) 2 …”

“…In the univariate case with the standard monomial basis, it is not difficult to recognize that the selected points are indeed the Leja points extracted from the mesh (cf. [2,13] and references therein). On the contrary, dependence on the ordering of the basis does not occur with the first algorithm, which is based on the notion of volume generated by the rows of a rectangular matrix (the two notions being eventually equivalent on the final square submatrix).…”