Multivariate Birkhoff-Lagrange interpolation schemes and Cartesian sets of nodes.
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...
Natural and smoothing quadratic spline. (An elementary approach)
For quadratic spine interpolating local integrals (mean-values) on a given mesh the conditions of existence and uniqueness, construction under various boundary conditions and other properties are studied. The extremal property of such's spline allows us to present an elementary construction and an algorithm for computing needed parameters of such quadratic spline smoothing given mean-values. Examples are given illustrating the results.
Natural Spline Functions, Their Associated Eigenvalue Problem.
Newton interpolating series at distinct points with coefficients in a real Banach algebra.
Newton Interpolation Is Efficient for Approximation of Linear Functionals.
Nonlinear Interpolation of Functions of Very Many Variables.
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,...
Obtaining a banded system of equations in complete spline interpolation problem via B-spline basis
We study the problem of interpolation by a complete spline of 2n − 1 degree given in B-spline representation. Explicit formulas for the first nand the last ncoefficients of B-spline decomposition are found. It is shown that other B-spline coefficients can be computed as a solution of a banded system of an equitype linear equations.
Od naměřených dat k jejich matematickému popisu pomocí funkce - a zase zpátky
On a mixed-type interpolation problem for real polynomials
On General Hermite Trigonometric Interpolation.
On Hermite interpolation in .
On Lagrange and Hermite Interpolation in Rk.
On one approach to local surface smoothing
A bicubic model for local smoothing of surfaces is constructed on the base of pivot points. Such an approach allows reducing the dimension of matrix of normal equations more than twice. The model enables to increase essentially the speed and stability of calculations. The algorithms, constructed by the aid of the offered model, can be used both in applications and the development of global methods for smoothing and approximation of surfaces.
On one method of numerical integration
The uniform convergence of a sequence of Lienhard approximation of a given continuous function is proved. Further, a method of numerical integration is derived which is based on the Lienhard interpolation method.
On optimal center locations for radial basis function interpolation: computational aspects.
On optimal triangular meshes for minimizing the gradient error.
On Richardson Extrapolation for Finite Difference Methods on Regular Grids.
On Samelson's Iteration for Factoring Polynomials.