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Restrictive splines for data processing

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Abstract

We propose a new type of polynomial spline for data processing — the restrictive spline. The construction of this type of spline generalizes known ones and differs from them by the fact that the conditions of matching the elements of the spline at its nodes contain restrictions (in the form of inequalities) on the value of the maximum permissible discontinuity of the matching derivative of corresponding order (standard splines do not contain such restrictions). Varying the strength of the restrictions, one can smoothly transform the spline from one defect to another through intermediate states, which do not exist for standard spines, extending the possibilities of the spline apaproximation. We propose a stable calculating scheme for constructing restrictive splines.

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Additional information

V. D. Kuznetsov Siberian Physics and Technology Institute of the Tomsk University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 128–135, September, 1992.

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Poddubnyi, V.V. Restrictive splines for data processing. Russ Phys J 35, 881–887 (1992). https://doi.org/10.1007/BF00560062

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Keywords

  • Data Processing
  • Intermediate State
  • Polynomial Spline
  • Standard Spine
  • Matching Derivative