Interpolation by natural cubic spline.

Kumar, Arun; Govil, L.K.

Displaying similar documents to “Interpolation by natural cubic spline.”

Natural and smoothing quadratic spline. (An elementary approach)

Jiří Kobza, Dušan Zápalka (1991)

Applications of Mathematics

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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.

Some properties of interpolating quadratic spline

Jiří Kobza (1990)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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Obtaining a banded system of equations in complete spline interpolation problem via B-spline basis

Yuriy Volkov (2012)

Open Mathematics

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We study the problem of interpolation by a complete spline of 2n − 1 degree given in B-spline representation. Explicit formulas for the first nand the last ncoefficients of B-spline decomposition are found. It is shown that other B-spline coefficients can be computed as a solution of a banded system of an equitype linear equations.

Fundamental quadratic splines and applications

Jiří Kobza, Radek Kučera (1993)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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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...

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...