Algorithms 70-71. Determination of a quadratic spline function with given values of the integrals in subintervals

E. Neuman

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Operator norm bounds and error bounds for quadratic spline interpolation

Martin Marsden (1979)

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Natural and smoothing quadratic spline. (An elementary approach)

Jiří Kobza, Dušan Zápalka (1991)

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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.

Algorithm 46. Determination of an interpolating quadratic spline function

E. Neuman (1976)

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Some properties of interpolating quadratic spline

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Quadratic splines smoothing the first derivatives

Jiří Kobza (1992)

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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.

A particular smooth interpolation that generates splines

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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...

A note on tension spline

Segeth, Karel

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Spline theory is mainly grounded on two approaches: the algebraic one (where splines are understood as piecewise smooth functions) and the variational one (where splines are obtained via minimization of quadratic functionals with constraints). We show that the general variational approach called smooth interpolation introduced by Talmi and Gilat covers not only the cubic spline but also the well known tension spline (called also spline in tension or spline with tension). We present the...