Error detection and correction in numerical computations
A simple analytical unified approach is described for error detection and correction in numerical computations. The computation process may be implemented by a computer program or memory or by a specialized digital or analog device. 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 and is based on algebraic concepts, such as transcendental degree of fielf extensions. 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 approach and other methods previously known.
Unable to display preview. Download preview PDF.
- Alexander Miczo "Digital Logic Testing and Simulation" Harper & RDW, Publishers, NY 1986.Google Scholar
- Michael O. Rabin "Efficient Dispersal of Information for Security, Load Balancing, and Fault Tolerance" Journal of the Association for Computing Machinery, Vol.36, No.2, April 1989, pp. 335–348.Google Scholar
- C.A. Asmuth and G.R. Blakley "Pooling, 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.Google Scholar
- Daniel P. Siewiorek and Robert S. Swarz "The Theory and Practice of Reliable System Design" Digital Press, 1982.Google Scholar
- M.G. Karpovsky "Error detection for polynomial computations" IEE.J.Comput.& Digital Tech., 1979, 2, (1), pp.49–56.Google Scholar
- M.G. Karpovsky "Testing for numerical computations" IEE. Proc. E, Comput.& Digital Tech., 1980, 127, (2), pp. 69–76.Google Scholar
- M.G. Karpovsky "Detection and location of errors by linear inequality checks", IEE PROC., Vol. 129, Pt. E, No.3, 1982.Google Scholar
- S. Lang "Algebra" Addison-Wesley Publishing Co., 1965.Google Scholar
- F.S. Vainstein "Irredundent linear checks for numerical computations" (to be published).Google Scholar