The complexity of interpolation attacks on block ciphers depends on the degree of the polynomial approximation and/or on the number of terms in the polynomial approximation expression. In some situations, the round function or the S-boxes of the block cipher are expressed explicitly in terms of algebraic function, yet in many other occasions the S-boxes are expressed in terms of their Boolean f...

Having various concrete industrial applications in mind we focus on surface fitting to large scattered data sets. We describe a general method for modelling data which incorporates both filtering using triangulations, and hierarchical interpolation based on compactly supported radial basis functions. The uniformity of the data points plays a significant role. The utility of the method is confir...

This contribution will touch the following topics: Short introduction into the theory of multivariate interpolation and approximation by nitely many (irregular) translates of a (not necessarily radial) basis function, motivated by optimal recovery of functions from discrete samples. Native spaces of functions associated to conditionally positive definite functions, and relations between such sp...

Multistep interpolation of scattered data by compactly supported radial basis functions requires hierarchical subsets of the data. This paper analyzes thinning algorithms for generating evenly distributed subsets of scattered data in a given domain in IR. AMS subject classification: 41A15, 65D05, 65D07.

Properties of the hybrid of block-pulse functions and Lagrange polynomials based on the Legendre-Gauss-type points are investigated and utilized to define the composite interpolation operator as an extension of the well-known Legendre interpolation operator. The uniqueness and interpolating properties are discussed and the corresponding differentiation matrix is also introduced. The appl...

Quasi-interpolation is a important tool, used both in theory and in practice, for the approximation of smooth functions from univariate or multivariate spaces which contain Πm = Πm(IR ) the d–variate polynomials of degree ≤ m. In particular, the reproduction of Πm leads to an approximation order of m + 1. Prominent examples include Lagrange and Bernstein type approximations by polynomials, the ...