Interpolation by Splines of Even Degree According to Subbotin and Marsden
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We consider the problem of interpolation by splines of even degree according to Subbotin and Marsden. The study is based on the representation of spline derivatives in the bases of normalized and nonnormalized B-splines. The systems of equations for the coefficients of these representations are obtained. The estimations of the derivatives of the error function in the approximation of an interpolated function by the complete spline are deduced via the norms of inverse matrices of the investigated systems of equations. The relationship between the splines in a sense of Subbotin and the splines in a sense of Marsden is established.
KeywordsInterpolation Spline Interpolation Problem Interpolation Point Divided Difference Interpolate Function
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- 5.S. B. Stechkin and Yu. N. Subbotin, “Additions,” in: J. H. Ahlberg, E. N. Nilson, and J. L. Walsh, The Theory of Splines and Their Applications [Russian translation], Mir, Moscow (1972), pp. 270–309.Google Scholar
- 6.S. B. Stechkin and Yu. N. Subbotin, Splines in Computational Mathematics [in Russian], Nauka, Moscow (1976).Google Scholar
- 8.Yu. S. Volkov, “On the construction of interpolation polynomial splines,” Vychislit. Sist., Issue 159, 3–18 (1997).Google Scholar
- 9.Yu. S. Volkov, “Completely nonnegative matrices in the methods of construction of interpolation splines of odd degree,” Mat. Trudy, 7, No. 2, 3–34 (2004).Google Scholar
- 10.F. R. Gantmakher and M. G. Krein, Oscillating Matrices and Kernels and Small Oscillations of Mechanical Systems [in Russian], Gostekhizdat, Moscow (1950).Google Scholar
- 12.Yu. S. Zav’yalov, B. I. Kvasov, and V. L. Miroshnichenko, Methods of Spline Functions [in Russian], Nauka, Moscow (1980).Google Scholar
- 16.Yu. S. Volkov, “Investigation of convergence of the process of interpolation for the derivatives of a complete spline,” Ukr. Mat. Visn., 9, No. 2, 278–296 (2012).Google Scholar
- 17.Yu. S. Volkov and V. T. Shevaldin, “Conditions for the preservation of form in the interpolation by Subbotin and Marsden splines of the second degree,” in: Proc. of the Institute of Mathematics and Mechanics, Ural Division of the Russian Academy of Sciences [in Russian], 18, No. 4, 145–152 (2012).Google Scholar
- 18.C. de Boor, T. Lyche, and L. L. Schumaker, “On calculating with B-splines, II. Integration,” in: Numerical Methods of Approximation Theory, Birkhäuser, Basel (1976), pp. 123–146.Google Scholar