A New Approach to Data Compression
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.
KeywordsInformation Data compression Interpolation Interlineation Interflatation Interstripation Intertubation Interlayeration Interlocation
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