Geodesic
Natural and smoothing quadratic spline. (An elementary approach)
Applications of Mathematics, Tome 36 (1991) no. 3, pp. 187-204.

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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.
DOI : 10.21136/AM.1991.104459
Classification : 41A15, 65D05, 65D07
Keywords: spline functions; quadratic spline; interpolation; smoothing by splines; histosplines; parabolic spline; cubic spline interpolation; natural spline interpolation 
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     title = {Natural and smoothing quadratic spline. {(An} elementary approach)},
     journal = {Applications of Mathematics},
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Kobza, Jiří; Zápalka, Dušan. Natural and smoothing quadratic spline. (An elementary approach). Applications of Mathematics, Tome 36 (1991) no. 3, pp. 187-204. doi : 10.21136/AM.1991.104459. http://geodesic.mathdoc.fr/articles/10.21136/AM.1991.104459/

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