Abstract
The idea of the method of data processing in this paper is to replace the data with operators that use functions (traces of unknown functions on the specified geometric objects such as points, lines, surfaces, stripes, tubes, or layers). This approach allows: first, to carry out data processing with parallelization of calculations; second, if the data are time dependent, to construct forecast operators at the functional level (extrapolation operators); third, to compress information. The paper will analyze the methods of constructing interlineation operators of functions of two or more variables, interflatation of functions of three or more variables, interpolation of functions of two or more variables, intertubation of functions of three or more variables, interlayeration of functions of three or more variables, interlocation of functions of two or more variables. Then, we will compare them with the interpolation operators of functions of corresponding number of variables.
The possibility of using known additional information about the investigated object as well as examples of objects or processes that allow to test the specified method of data processing in practice. Examples are given of constructing interpolation operators of the function of many variables using interlineation and interflatation, which require less data about the approximate function than operators of classical spline-interpolation. In this case, the order of accuracy of the approximation is preserved.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Radon, J.: Uber die Bestimmung von Functionen durch ihre Integralverte l ngs gewisser Manningfaltigkeiten. Berichte Sachsische Academieder Wissenschaften. Leipzig, Mathem. - Phys. K1. 69, 262–267 (1917)
Sergienko, I.V., Lytvyn, O.M.: New information operators in mathematical modeling (a review). Cybern. Syst. Anal. 54(1), 21–30 (2018)
Lytvyn, O.M.: Interlineation functions and some of its applications, 545 p. Osnova, Kharkiv (2002). (in Ukrainian)
Powell, W.B.: Approximate Dynamic Programming: Solving the Curses of Dimensionality. Wiley, Hoboken (2007). ISBN 0-470-17155-3
Lytvyn, O.N., Nechuiviter, O.P.: 3D Fourier coefficients on the class of differentiable functions and spline interflatation. J. Autom. Inf. Sci. 44(3), 45–56 (2012)
Lytvyn, O.N., Pershina, Y.I., Sergienko, I.V.: Estimation of discontinuous functions of two variables with unknown discontinuity lines (rectangular elements). Cybern. Syst. Anal. 50(4), 594–602 (2014)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this paper
Cite this paper
Lytvyn, O.M., Lytvyn, O.O. (2019). A New Approach to Data Compression. In: Chertov, O., Mylovanov, T., Kondratenko, Y., Kacprzyk, J., Kreinovich, V., Stefanuk, V. (eds) Recent Developments in Data Science and Intelligent Analysis of Information. ICDSIAI 2018. Advances in Intelligent Systems and Computing, vol 836. Springer, Cham. https://doi.org/10.1007/978-3-319-97885-7_37
Download citation
DOI: https://doi.org/10.1007/978-3-319-97885-7_37
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-97884-0
Online ISBN: 978-3-319-97885-7
eBook Packages: Intelligent Technologies and RoboticsIntelligent Technologies and Robotics (R0)