matrix algebra

The purpose of this work is to develop and comprehensively study effective methods of using vector algebra tools to solve practical problems of information coding with the integration of modern computing technologies aimed at increasing the productivity, reliability and adaptability of the corresponding systems. In the light of the rapid development of information technologies and the growth of the volume of data that needs protection, it becomes relevant to design algorithms, which would provide not only security, but also the best speed in real time.

A method of local interpolation of tabular functions from one independent variable using the Taylor polynomial of the nth degree in arbitrarily located interpolation nodes has been developed. This makes it possible to calculate intermediate values of tabular functions between interpolation nodes. The conducted analysis of the latest research and publications in the field of interpolation of tabular functions showed that the main part of the research is a strict theory of interpolation, i.e. clarification of its fundamental mathematical provisions.