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Interpolating and smoothing biquadratic spline

Radek Kučera (1995)

Applications of Mathematics

The paper deals with the biquadratic splines and their use for the interpolation in two variables on the rectangular mesh. The possibilities are shown how to interpolate function values, values of the partial derivative or values of the mixed derivative. Further, the so-called smoothing biquadratic splines are defined and the algorithms for their computation are described. All of these biquadratic splines are derived by means of the tensor product of the linear spaces of the quadratic splines and...

Interpolation and integration based on averaged values

Borislav Bojanov (2006)

Banach Center Publications

We discuss recent results on constructing approximating schemes based on averaged values of the approximated function f over linear segments. In particular, we describe interpolation and integration formulae of high algebraic degree of precision that use weighted integrals of f over non-overlapping subintervals of the real line. The quadrature formula of this type of highest algebraic degree of precision is characterized.

Interpolation by bivariate polynomials based on Radon projections

B. Bojanov, I. K. Georgieva (2004)

Studia Mathematica

For any given set of angles θ₀ < ... < θₙ in [0,π), we show that a set of n + 2 2 Radon projections, consisting of k parallel X-ray beams in each direction θ k , k = 0, ..., n, determines uniquely algebraic polynomials of degree n in two variables.

Interpolation formulas for functions of exponential type

Josef Kofroň, Emílie Moravcová (2001)

Applications of Mathematics

In the paper we present a derivative-free estimate of the remainder of an arbitrary interpolation rule on the class of entire functions which, moreover, belong to the space L ( - ∞ , + ∞ ) 2 . The theory is based on the use of the Paley-Wiener theorem. The essential advantage of this method is the fact that the estimate of the remainder is formed by a product of two terms. The first term depends on the rule only while the second depends on the interpolated function only. The obtained estimate of the remainder of...

Interpolation harmonique

Patrick Rabier (1977)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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