On a theorem which limits the number of mixed interpolated derivatives for some plane regular uniform rectangular Birkhoff interpolation schemes.
Numerical characteristics of uniform Birkhoff univariate interpolation schemes.
Generalized Birkhoff interpolation schemes: conditions for almost regularity.
Inferior and superior sets with respect to an arbitrary set from used in the multidimensional interpolation theory.
Necessary and sufficient conditions for almost regularity of uniform Birkfoff interpolation schemes.
UR Birkhoff interpolation with rectangular sets of derivatives
In this paper we characterize the regular UR Birkhoff interpolation schemes ( uniform, rectangular sets of nodes) with rectangular sets of derivatives, and beyond.
Normal bivariate Birkhoff interpolation schemes and Pell equation
Finding the normal Birkhoff interpolation schemes where the interpolation space and the set of derivatives both have a given regular “shape” often amounts to number-theoretic equations. In this paper we discuss the relevance of the Pell equation to the normality of bivariate schemes for different types of “shapes”. In particular, when looking at triangular shapes, we will see that the conjecture in Lorentz R.A., , Lecture Notes in Mathematics, 1516, Springer, Berlin-Heidelberg, 1992, is not satisfied,...
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