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Multivariate smooth interpolation that employs polyharmonic functions

Segeth, Karel (2019)

Programs and Algorithms of Numerical Mathematics

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)

Jiří Kobza, Dušan Zápalka (1991)

Applications of Mathematics

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.

Normal bivariate Birkhoff interpolation schemes and Pell equation

Marius Crainic, Nicolae Crainic (2009)

Commentationes Mathematicae Universitatis Carolinae

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,...

On one approach to local surface smoothing

Nikolay Dikoussar, Csaba Török (2007)

Kybernetika

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

Josef Matušů, Gejza Dohnal, Martin Matušů (1991)

Applications of Mathematics

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 semiregular families of triangulations and linear interpolation

Michal Křížek (1991)

Applications of Mathematics

We consider triangulations formed by triangular elements. For the standard linear interpolation operator π h we prove the interpolation order to be v - π h v 1 , p ≤ C h v 2 , p for p > 1 provided the corresponding family of triangulations is only semiregular. In such a case the well-known Zlámal’s condition upon the minimum angle need not be satisfied.

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