THE CALCULATION OF TRIPLE INTEGRALS OF HIGHLY OSCILLATORY FUNCTIONS WITH USING INTERFLATATION
Abstract
Today a new data, such as traces of the function on a system of lines or planes, are considered in mathematical models in solving of problems of three-dimensional computer tomography, digital signal processing and in many others. In this article cubature formula of the calculation of high oscillating integrals is presented by using operators of spline-interflatation in the case when information about function is set of values on the perpendicular flats. The estimation of error of approaching of the cubature formula is getting on Gelder’s class of functions. It is proved that this evaluation can also be obtained through the error estimates corresponding quadrature formulas.
About the Authors
O. . Lytvyn
Ukrainian Engineering and Pedagogical Academy
Russian Federation
Russian Federation
O. . Nechuiviter
Ukrainian Engineering and Pedagogical Academy
Russian Federation
Russian Federation
References
1. Чахкиев М.А. Оценки осциллирующих интегралов с выпуклой фазой // Изв. РАН. Сер. Матем. 2006. Т. 70. №1. С. 183-220.
2. Литвин О.М. Інтерлінація функцій та деякі її застосування. Харків.: Основа, 2002. 544 с.
3. Gal S.G., Szabados J. On the preservation of global smoothness by some interpolation operators // Studio, Scientiarum Mathematicarum Hungarica 35 (1999), 391'1, 14. P. 397-414.
4. Iserles A., Norsett S. P. From high oscillation to rapid approximation III: Multivariate expansions, Technical Report NA2007/01, DAMPT, University of Cambridge, 2007. р. 37.
5. Iserles A., Norsett S. P. From high oscillation to rapid approximation IV:Accelerating convergence, Technical Report NA2007/07, DAMPT, University of Cambridge, 2007. р. 24.
6. Lytvyn Oleg N., Nechuyviter Olesya P. Methods in the multivariate digital signal processing with using spline-interlineation: рroceeding of the IASTED International Conferences on Automation, Control, and Information Technology, ASIT 2010, 1518.06.2010. Novosibirsk, 2010. P. 90 96.
7. Lytvyn, O.N., Nechuyviter O.P. 3D Fourier Coefficients on the Class of Differentiable Functions and Spline Interflatation // Journal of Automation and Information Sciences. 2012. Vol. 44, № 3. P. 45-56.
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