Interpolation at a Few Points

Rational Interpolation at Chebyshev points

The Lanczos method and its variants can be used to solve eeciently the rational interpolation problem. In this paper we present a suitable fast modiication of a general look-ahed version of the Lanczos process in order to deal with polynomials expressed in the Chebyshev orthogonal basis. The proposed approach is particularly suited for rational interpolation at Chebyshev points, that is, at the...

Single Nucleotide Polymorphisms and Association Studies: A Few Critical Points

Uncovering DNA sequence variations that correlate with phenotypic changes, e.g., diseases, is the aim of sequence variation studies. Common types sequence variations are Single nucleotide polymorphism (SNP, pronounced snip).SNPs are the third-generation molecular marker. SNP represents a DNA sequence variant of a single base pair with the minor allele occurring in more than 1% of a given popula...

Interpolation at Equidistant Points by a Sum of Exponential Functions

A set of necessary and suflicient conditions for the existence and uniqueness of a solution to the problem of interpolation at equidistant points by a sum of exponential functions is given. Simultaneously a simple method for constructing the solution is developed. The confluent interpolation problem in which all the points of interpolation coincide is dealt with similarly. Integral representati...

Hyperinterpolation at Xu Points and Interpolation at Padua Points in the Square: Computational Aspects

Embedding Vertices at Points: Few Bends Suffice for Planar Graphs

The existing literature gives efficient algorithms for mapping trees or less restrictively outerplanar graphs on a given set of points in a plane, so that the edges are drawn planar and as straight lines. We relax the latter requirement and allow very few bends on each edge while considering general plane graphs. Our results show two algorithms for mapping four-connected plane graphs with at mo...