Abstract
Modern development of many technical areas is characterized by the rapid introduction of new digital technologies, algorithms, and methods which contribute to the emergence of latest approaches to obtaining, processing and analyzing information. It leads to further creation of new numerical methods for solving corresponding issues. Thereupon, there arises a problem of building new or improving known mathematical models, as well as their effective computer implementation. Depending on the modeling type the methods of probability theory and mathematical statistics, one- and mul- tidimensional interpolation and approximation theory are widely used in the process of preparing information. Along with the tasks of multidimen- sional interpolation, operators that restore intermediate values of quantities from an existing set of known data are widely used in the construction of mathematical models of various processes, in particular, when the values of a function of many variables on lines, planes, etc. are known. An example of the effective use of the above operators is the theory of calculating integrals of highly oscillating functions of many variables since the algorithm is chosen depending on the type of information about the functions. The author of this theory is the Laureate of the State Prize of Ukraine in Science and Technology, Doctor of Physical and Mathematical Sciences, Professor O.M. Lytvyn. The purpose of this article is to review the results of applying the theory of new information operators to the calculation of integrals of fast oscillating functions of many variables, as well as to present a new cubature formula for the approximate calculation of double integrals of fast oscillating functions of general type. The cubature formula is effective in terms of using the input information to achieve a given accuracy.
Published Version
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call