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Low redundancy polynomial checks for numerical computation

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Applicable Algebra in Engineering, Communication and Computing Aims and scope

Abstract

This paper presents a new approach to detection and correction of errors in numerical computations caused by both software and/or hardware faults. This approach does not depend on the form of representation or on the specific features of the implementation of a program or a device computing the given function. The described approach results in a substantial reduction of the hardware overhead required for multiple error detection and correction as compared to the check sum method or other methods previously known.

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References

  1. Lala Parag K.: Fault Tolerant & Fault Testable Hardware design. Prentice-Hall International, London 1985

    Google Scholar 

  2. Blakley, G. R., Meadows, C.: Security of Ramp Schemes pp. 242–268 in the book “Advances in Cryptology: Proceedings of Cripto 84. Blakley G. R., Chaum, D. (eds) Vol. 196 of Lecture Notes in Computer Science). Berlin, Heidelberg, New York: Springer 1985

    Google Scholar 

  3. Asumth, C. A. Blakley, G. R.: Polling splitting and restituting information to overcome total failure of some channels of communication. Proc. of the 1982 Symposium on Security and Privacy. IEEE Society, pp. 156–169

  4. Siewiorek, D. P., Swarz, R. S.: The Theory and Practice of Reliable System Design, Digital Press, 1982

  5. Karpovsky, M. G.: Error Detection for Polynomial Computations. IEEE J. Comput. Digital Tech. 2, (1), 49–56 (1979)

    Google Scholar 

  6. Karpovsky, M. G.: Testing for Numerical Computations, IEEE Proc. E. Comput. Digital Tech. 127, (2), 69–76 (1980)

    Google Scholar 

  7. Karpovsky, M. G.: Detection and Location of errors by Linear Inequality Checks. IEEE Proc, vol. 129, Pt. E, No. 3, 1982

  8. Lang, S.: Algebra London: Addison-Wesley 1992

    Google Scholar 

  9. Vainstein, F. S.: Error Detection and Correction in Numerical Computations by Algebraic Methods. Lecture Notes in Computer Science vol. 539. Berlin, Heidelberg, New York: Springer 1991

    Google Scholar 

  10. Blum, M., Kannan, S.: Designing Programs That Check Their Work. 21st ACM Symposium on Theory of Computing, pp. 86–97 (1989)

  11. Blum, M., Luby, M., Rubinfeld, R.: Self-Testing and Self-Correcting Programs with Applications to Numerical Problems, 22nd ACM Symposium on Theory of Computing, pp. 73–83 (1990)

  12. Moore, R. E.: Methods and Applications of Interval Analysis, SIAM, Philadelphia, 1979

    Google Scholar 

  13. Neumaier, A.: Interval Methods for Systems of Equations, Cambridge University Press (1990)

Download references

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  1. Department of Electrical Engineering 551 McNair Hall, North Carolina A&T State University, 27411, Greensboro, NC, USA

    F. S. Vainstein

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  1. F. S. Vainstein
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Vainstein, F.S. Low redundancy polynomial checks for numerical computation. AAECC 7, 439–447 (1996). https://doi.org/10.1007/BF01293262

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  • DOI: https://doi.org/10.1007/BF01293262

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