Geodesic
Form preservation under approximation by local exponential splines of an arbitrary order
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 17 (2011) no. 3, pp. 291-299
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We continue the study of the properties of local $\mathcal L$-splines with uniform knots (such splines were constructed in the authors' earlier papers) corresponding to a linear differential operator $\mathcal L$ of order $r$ with constant coefficients and real pairwise distinct roots of the characteristic polynomial. Sufficient conditions (which are also necessary) are established under which the $\mathcal L$-spline locally inherits the property of the generalized $k$-monotonicity of $(k\le r-1)$ input data, which are the values of the approximated function at the nodes of a uniform grid shifted with respect to the grid of knots of the $\mathcal L$-spline. The parameters of an $\mathcal L$-spline that is exact on the kernel of the operator $\mathcal L$ are written explicitly.
Keywords: form preservation, $k$-monotonicity, local $\mathcal L$-spline. 
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E. V. Strelkova; V. T. Shevaldin. Form preservation under approximation by local exponential splines of an arbitrary order. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 17 (2011) no. 3, pp. 291-299. http://geodesic.mathdoc.fr/item/TIMM_2011_17_3_a28/

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