Mémoire sur le calcul fonctionnel distributif
Modified Specht's plate bending element and its convergence analysis.
Multivariate Birkhoff-Lagrange interpolation schemes and Cartesian sets of nodes.
Multivariate interpolation II of Langrange and Hermite type
Multivariate smooth interpolation that employs polyharmonic functions
We study the problem of construction of the smooth interpolation formula presented as the minimizer of suitable functionals subject to interpolation constraints. We present a procedure for determining the interpolation formula that in a natural way leads to a linear combination of polyharmonic splines complemented with lower order polynomial terms. In general, such formulae can be very useful e.g. in geographic information systems or computer aided geometric design. A simple computational example...
Multivariate spline functions, B-spline bases and polynomial interpolations II
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...
On a boundary value problem of the fourth order
On a mixed-type interpolation problem for real polynomials
On a new kind of 2-periodic trigonometric interpolation
It is well-known that the interpolation theory plays an important role in many fields of computer vision, especially in surface reconstruction. In this paper, we introduce a new kind of 2-period interpolation of functions with period . We find out the necessary and sufficient conditions for regularity of this new interpolation problem. Moreover, a closed form expression for the interpolation polynomial is given. Our interpolation is of practical significance. Our results provide the theoretical...
On a subclass of functions for which the Lagrange interpolation yields the Jackson order of approximation.
On a theorem which limits the number of mixed interpolated derivatives for some plane regular uniform rectangular Birkhoff interpolation schemes.
On an Interpolation Process of Lagrange-Hermite Type
On approximation by Chebyshevian box splines
Chebyshevian box splines were introduced in [5]. The purpose of this paper is to show some new properties of them in the case when the weight functions are of the form , where the functions are periodic functions of one variable. Then we consider the problem of approximation of continuous functions by Chebyshevian box splines.