Necessary and sufficient conditions for almost regularity of uniform Birkfoff interpolation schemes.
New error inequalities for the Lagrange interpolating polynomial.
Newton interpolating series at distinct points with coefficients in a real Banach algebra.
Non-linear Fractal Interpolating Functions
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., Multivariate Birkhoff Interpolation, Lecture Notes in Mathematics, 1516, Springer, Berlin-Heidelberg,...
Numerical characteristics of uniform Birkhoff univariate interpolation schemes.
Numerical curves and their applications to algebraic curves
Hermite interpolation by bivariate algebraic polynomials and its applications to some problems of the theory of algebraic curves, such as the existence of algebraic curves with given singularities, is considered. The scheme , i.e., the sequence of multiplicities of nodes associated with the degree of interpolating polynomials, is considered. We continue the investigation of canonical decomposition of schemes and define so called maximal schemes. Some numerical results concerning the factorization...