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Cubic splines with minimal norm

Jiří Kobza — 2002

Applications of Mathematics

Natural cubic interpolatory splines are known to have a minimal L 2 -norm of its second derivative on the C 2 (or W 2 2 ) class of interpolants. We consider cubic splines which minimize some other norms (or functionals) on the class of interpolatory cubic splines only. The cases of classical cubic splines with defect one (interpolation of function values) and of Hermite C 1 splines (interpolation of function values and first derivatives) with spline knots different from the points of interpolation are discussed....

Quadratic splines smoothing the first derivatives

Jiří Kobza — 1992

Applications of Mathematics

The extremal property of quadratic splines interpolating the first derivatives is proved. Quadratic spline smoothing the given values of the first derivative, depending on the knot weights w i and smoothing parameter α , is then studied. The algorithm for computing appropriate parameters of such splines is given and the dependence on the smoothing parameter α is mentioned.

An algorithm for biparabolic spline

Jiří Kobza — 1987

Aplikace matematiky

The paper deals with the computation of suitably chosen parameters of a biparabolic spline (ot the tensor product type) on a rectangular domain. Some possibilities of choosing such local parameters (concentrated, dispersed parameters) are discussed. The algorithms for computation of dispersed parameters (using the first derivative representation) and concentraced parameters (using the second derivative representation) are given. Both these algorithms repeatedly use the one-dimensional algorithms....

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