Displaying similar documents to “On the application of the orthonormal Franklin system to the approximation of analytic functions”

A particular smooth interpolation that generates splines

Segeth, Karel

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There are two grounds the spline theory stems from - the algebraic one (where splines are understood as piecewise smooth functions satisfying some continuity conditions) and the variational one (where splines are obtained via minimization of some quadratic functionals with constraints). We use the general variational approach called smooth interpolation introduced by Talmi and Gilat and show that it covers not only the cubic spline and its 2D and 3D analogues but also the well known...

Cubic splines with minimal norm

Jiří Kobza (2002)

Applications of Mathematics

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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...