Approximate calculation of double integrals from rapidly oscillating functions of the general form
Keywords:
кубатурна формула, інтеграл від швидкоосцилюючої функції загального виду, клас диференційованих функційAbstract
The current state of development of information technologies encourages scientists to improve mathematical models of phenomena and processes in many areas of technical direction. In particular, modern methods of digital processing of signals and images use algorithms with new information operators. Cubature formulas for the approximate calculation of integrals from rapidly oscillating functions of many variables for different types of data are constructed. The paper investigates the approximate calculation of double integrals of the general form on the class of differential functions. A new cubature formula is proposed, it uses piecewise linear splines as auxiliary functions. Information about the functions is given by traces on the corresponding lines. It is proved that the cubature formula is optimal in order of accuracy.
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