2021, issue 3, p. 43-52
Received 22.06.2021; Revised 26.07.2021; Accepted 28.09.2021
Published 30.09.2021; First Online 25.10.2021
https://doi.org/10.34229/2707-451X.21.3.4
Previous | Full text (in Ukrainian) | Next
Using Rounding Errors in Modern Computer Technologies
Valerii
Zadiraka 
,
Inna Shvidchenko *
V.M. Glushkov Institute of Cybernetics of the NAS of Ukraine, Kyiv
* Correspondence: This email address is being protected from spambots. You need JavaScript enabled to view it.
Introduction. When solving problems of transcomputational complexity, the problem of evaluating the rounding error is relevant, since it can be dominant in evaluating the accuracy of solving the problem.
The ways to reduce it are important, as are the reserves for optimizing the algorithms for solving the problem in terms of accuracy. In this case, you need to take into account the rounding-off rules and calculation modes.
The article shows how the estimates of the rounding error can be used in modern computer technologies for solving problems of computational, applied mathematics, as well as information security.
The purpose of the article is to draw the attention of the specialists in computational and applied mathematics to the need to take into account the rounding error when analyzing the quality of the approximate solution of problems. This is important for mathematical modeling problems, problems using Bigdata, digital signal and image processing, cybersecurity, and many others.
The article demonstrates specific estimates of the rounding error for solving a number of problems: estimating the mathematical expectation, calculating the discrete Fourier transform, using multi-digit arithmetic and using the estimates of the rounding error in algorithms for solving computer steganography problems.
The results. The estimates of the rounding error of the algorithms for solving the above-mentioned classes of problems are given for different rounding-off rules and for different calculation modes.
For the problem of constructing computer steganography, the use of the estimates of the rounding error in computer technologies for solving problems of hidden information transfer is shown.
Conclusions. Taking into account the rounding error is an important factor in assessing the accuracy of the approximate solution of problems of the complexity above average.
Keywords: rounding error, computer technology, discrete Fourier transform, multi-digit arithmetic, computer steganography.
Cite as: Zadiraka V., Shvidchenko I. Using Rounding Errors in Modern Computer Technologies. Cybernetics and Computer Technologies. 2021. 3. P. 43–52. (in Ukrainian) https://doi.org/10.34229/2707-451X.21.3.4
References
1. Ivanov V.V. Computer calculation methods: Reference guide. Kiev: Nauk. dumka, 1986. 584 p. (in Russian)
2. Voevodin V.V. Rounding errors and stability in direct methods of linear algebra. M.: VC MGU, 1969. 154 p. (in Russian)
3. Uilkinson Dzh.H. Algebraic eigenvalue problem. M.: Nauka, 1970. 564 p. (in Russian)
4. Ramos G.U. Roundoff error analysis of the fast Fourier transform. Mathematics of Computation. 1971. 25 (116). P. 757–768. https://doi.org/10.1090/S0025-5718-1971-0300488-0
5. Weinstein C.J. Roundoff noise in floating point fast Fourier transform computation. IEEE Trans. Audio and Electroaconst. 1969. 19 (2). P. 209–215. https://doi.org/10.1109/TAU.1969.1162049
6. Zadiraka V.K., Oleksiuk O.S. Computer arithmetic of multi-digit numbers. Naukove vydannia. K.: 2003. 264 p. (in Ukraine)
7. Zadiraka V.K., Melnykova S.S., Tereshchenko A.M. On the asymptotic efficiency of the Schenhage-Strassen algorithm. Pratsi mizhnar. konf. «Pytannia optymizatsii obchyslen (POO-XXXII)», prysviach. 75-richchiu vid dnia narodzhennia akademika V.S. Mykhalevycha. K.: In-t kibernetyky im. V.M. Hlushkova NAN Ukrainy, 2005. P. 82–83. (in Ukraine)
8. Zadiraka V.K., Tereshchenko A.M. Computer arithmetic of multi-digit numbers in sequential and parallel computational models. K.: Nauk. dumka, 2021. 136 p. (in Ukraine)
9. Zadiraka V.K., Melnikova S.S., Borodavka N.V. Spectral algorithms of computer steganography. Iskusstvennyj intellekt. 2002. 3. P. 532–541. http://iai.dn.ua/public/JournalAI_2002_3/Razdel4/11_Zadiraka_spektralni.pdf (in Ukraine)
10. Zadiraka V.K., Shvidchenko I.V. The influence of the quality of the estimation of the rounding error of the steganographic algorithm on its resistance. Matematychne ta kompiuterne modeliuvannia. Seriia: Fizyko-matematychni nauky. 2015. 12. P. 101–112. http://dspace.nbuv.gov.ua/bitstream/handle/123456789/133865/10-Zadiraka.pdf?sequence=1 (in Russian)
ISSN 2707-451X (Online)
ISSN 2707-4501 (Print)
Previous | Full text (in Ukrainian) | Next