Yu.S. Volkov. Shape preserving conditions for integro quadratic spline interpolation in the mean ... P. 71-77

Earlier, Yu. N. Subbotin considered the problem of interpolation in the mean, where the interpolated values of the function are replaced by averaged values on an interval. In his paper, the grid was uniform, but the space grid step could differ from the size of the averaging intervals. Subbotin investigated the existence of such splines and their convergence in different metrics. In the literature, splines of this type are also called integro or histosplines. The present paper considers such an interpolating in the mean quadratic spline on an arbitrary nonuniform grid of a closed interval, where the averaging intervals are the grid intervals. Sufficient conditions are obtained for the inheritance by an integro spline of certain properties of the approximated function such as nonnegativity, monotonicity, and convexity.

Keywords: integro spline, interpolation in the mean, shape preserving, quadratic splines

Received August 14, 2022

Revised September 5, 2022

Accepted September 12, 2022

Funding Agency: This work was carried out under a state contract of the Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences (project no. FWNF–2022–0015).

Yuriy Stepanovich Volkov, Dr. Phys.-Math. Sci., Prof., Sobolev Institute of Mathematics of the Siberian Branch of the Russian Academy of Sciences, Novosibirsk, 630090 Russia, e-mail: volkov@math.nsc.ru

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Cite this article as: Yu.S. Volkov. Shape preserving conditions for integro quadratic spline interpolation in the mean. Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2022, vol. 28, no. 4, pp. 71–77; Proceedings of the Steklov Institute of Mathematics (Suppl.), 2022, Vol. 319, Suppl. 1, pp. S291–S197.