Modified Hermitian splines
Keywords:
interpolation, spline, trigonometric interpolation, vibration resonanceAbstract
Modified Hermite trigonometric splines, which provide more accurate result of interpolation by comparison with existing methods for quasi-periodic functions and vibrational resonance, are suggested in the article. The main areas of application of the developed method of interpolation are identified. To test the adequacy of the developed spline authors present a table comparing the deviations of the interpolated test functions using the proposed and known methods of spline interpolation.References
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2. Maksimov A. O. On the subharmonic emission of gas bubbles under two-frequency excitation / A. O. Maksimov // Ultrasonics. — 1997. — Vol 34. — P. 79—86.
3. Victor J. D. Two-frequency analysis of interactions elicited by Vernier stimuli / J. D. Victor, M. M. Conte // Visual Neuroscience. — 2000. — № 17.
4. Su D. C. Simple two-frequency laser / D. C. Su, M. H. Chiu, C. D. Chen //Precision Engineering. — 1996. — Vol 18.
5. Vibrational resonance in a noise-induced structure /[A. A. Zaikin, L. Lόpez, J. P. Baltanás, and other] // Phys. Rev. — 2002. — E66.
6. Квєтний Р. Н. Основи моделювання та обчислювальних методів / Р. Н. Квєтний. — Вінниця : ВНТУ. — 2007. — 150 с.
7. Renka R. J. Interpolatory tension splines with automatic selection of tension factors / R. J. Renka // SIAM Journal of Scientific and Statistical Computing. — 1987. — Vol 8. — P. 393—415.
8. Farin G. Curves and Surfaces for Computer Aided Geometric Design / G. Farin. — San Diego : Academic Press. — 1993.
9. Farin G. NURB Curves and Surfaces : From Projective Geometry to Practical Use / G. Farin. — PetersPress, 1995.
10. Herriot J. G. Procedures for Quintic Natural Spline Interpolation / J. G. Herriot, C. H. Reinsch // Association for Computing Machinery, Transactions on Mathematical Software. — 1976. — Vol. 2. — № 3.
11. Blanc C. X-Splines : A Spline Model Designed for the End-User / C. Blanc, C. Schlick // Laboratoire Bordelais de Recherche en Informatique.
12. Restrepo J. Introduction to scientific computing / J. Restrepo // Numerical Analysis & Scientific Computing. — 2001. — № 1. — P. 128—137.
13. Bourke P. Interpolation methods / Bourke P. // Miscellaneous : projection, modelling, rendering. — 1999. — № 1.
14. Kauffmann R. F. Implementing Uniform Trigonometric Spline Curves / R. F. Kauffmann // Dobbs Portal. Architecture&Design. — 2007. — № 1. — P. 1—9.
15. Квєтний Р. Н. Тригонометрична інтерполяція сплайнами / Р. Н. Квєтний, В. Ю. Дементьєв // Вісник Вінницького політехнічного інституту. — 2008. — № 5. — С. 67—68.
16. Мамфорд Д. Лекции о тета-функциях / Д. Мамфорд. — М. : Мир. — 1988. — 448 с.
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Published
2010-11-12
How to Cite
[1]
R. N. Kvietnyi and V. Y. Dementyev, “Modified Hermitian splines”, Вісник ВПІ, no. 3, pp. 173–176, Nov. 2010.
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Information technologies and computer sciences
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