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Ideal interpolation: Mourrain's condition vs. D-invariance

C. de Boor (2006)

Banach Center Publications

Mourrain [Mo] characterizes those linear projectors on a finite-dimensional polynomial space that can be extended to an ideal projector, i.e., a projector on polynomials whose kernel is an ideal. This is important in the construction of normal form algorithms for a polynomial ideal. Mourrain's characterization requires the polynomial space to be 'connected to 1', a condition that is implied by D-invariance in case the polynomial space is spanned by monomials. We give examples to show that, for more...

Interpolants d'Hermite C2 obtenus par subdivision

Jean-Louis Merrien (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

We propose a two point subdivision scheme with parameters to draw curves that satisfy Hermite conditions at both ends of [a,b]. We build three functions f,p and s on dyadic numbers and, using infinite products of matrices, we prove that, under assumptions on the parameters, these functions can be extended by continuity on [a,b], with f'=p and f''=s .

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.

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