A subdivision scheme for constructing smooth surfaces interpolating scattered data in 1~3 is proposed. It is also possible to impose derivative constraints in these points. In the case of functional data, i,e., data are given in a properly triangulated set of points {(x~, y~)}~=~ from which none of the pairs (xi, Yi) and (x j, gj) with i ~ j coincide, it is proved that the resulting surface (fu...

Bivariate means defined as the Schwab-Borchardt mean of two bivariate means are investigated. Explicit formulas for those means are obtained. It is demonstrated that they interpolate inequalities connecting the well known bivariate means. Optimal bounds for the means under discussion are also obtained. The bounding quantities are convex combinations of the generating means.

Recently it is observed that the generalized exponential distribution can be used quite effectively to analyze lifetime data in one dimension. The main aim of this paper is to define a bivariate generalized exponential distribution so that the marginals have generalized exponential distributions. It is observed that the joint probability density function, the joint cumulative distribution funct...

This paper introduces new classes of bivariate time series models being useful to fit count data time series with a finite range of counts. Motivation comes mainly from the comparison of schemes for monitoring tourism demand, stock data, production and environmental processes. All models are based on the bivariate binomial distribution of Type II. First, a new family of bivariate integer-valued...

A definition of bivariate matrix functions is introduced and some theoretical as well as algorithmic aspects are analyzed. It is shown that our framework naturally extends the usual notion of (univariate) matrix functions and allows to unify existing results on linear matrix equations and derivatives of matrix functions. Mathematics subject classification (2010): 15A16, 15A24, 15A69.

Recently, L. Breiman and l.R. Friedman introduced a non-parametric method for estimating transformations in regression data, the so called ACE-algorithm. This method promises to become one of the most powerful tools in data analysis, if some pitfalls are avoided. We point out some unexpected features in ACE as well as some curiosities in its mathematics which relate to tomography and projection...

We extend the Shepard-Bernoulli operators introduced in [1] to the bivariate case. These new interpolation operators are realized by using local support basis functions introduced in [2] instead of classical Shepard basis functions and the bivariate three point extension [3] of the generalized Taylor polynomial introduced by F. Costabile in [4]. The new operators do not require either the use o...