Literature Cited
V. V. Voevodin, Numerical foundations of Linear Algebra [in Russian], Nauka, Moscow (1977).
I. N. Molchanov, On certain difficulties in the solving of applied problems on computers. Preprint No. 79–5, Inst. of Cybernetics, Academy of Sciences of the Ukrainian SSR, Kiev (1979).
J. H. Wilkinson, The Algebraic Eigenvalue Problem, Claredon Press, Oxford (1965).
B. N. Parlett, The Symmetric Eigenvalue Problem, Prentice-Hall, Englewood Cliffs (1980).
G. E. Eorsythe, M. A. Malcom, and C. B. Moler, Computer Methods for Mathematical Computations, Prentice-Hall, Englewood Cliffs (1977).
V. V. Voevodin, Certain computer aspects of the parallellization of computations. Mathematical Seminar, “Problems of Numerical Mathematics,” Preprint No. 22, VINITI, Moscow (1981).
I. Mikloshko, “Relation between algorithms, programs, and the structure of parallel computers,” in: Algorithms, Software, and the Architecture of Computational Systems, [in Russian], Nauka, Moscow (1982), pp. 6–36.
D. J. Evans (ed.), Parallel Processing Systems, Cambridge University Press, Cambrridge (1982).
I. V. Prangishvili, Microprocessors and Local Nets of Microcomputers in Distributed Control Systems [in Russian], Energoatomizdat, Moscow (1985).
I. Mikloshko, “The complexity of parallel algorithms,” in: Algorithms, software, and the Architecture of Microprocessor Computational Systems [in Russian], Nauka, Moscow (1982), pp. 241–253.
V. I. Solodovnikov, “Upper bounds of complexity of the solution of systems of linear equations,” Zap. Nauchn. Sem. Leningr. Otd. Mat. Inst.,118, 159–187 (1982).
G. A. Korn and T. M. Korn, Mathematical Handbook for Scientists and Engineers, McGraw-Hill, New York (1961).
V. N. Faddeeva and D. K. Faddeev, “Parallel calculations in linear algebra,” Kibernetika, No. 6, 28–40 (1977).
V. N. Faddeeva and D. K. Faddeev, “Parallel calculations in linear algebra. II,” Kibernetika, No. 3, 18–31 (1982).
Ya. E. Romm, Parallel stable variant of the Leverrier-Faddeev method. TRTI (1985). Manuscript deposited with VINITI, No. 5005-85, July 12, 1985.
Ya. E. Romm, “On the acceleration of linear stationary iterative processes in multiprocessor computers. I,” Kibernetika., No. 1, 47–54 (1982).
Ya. E. Romm, “On the acceleration of linear stationary iterative processes in multiprocessor computers. II,” Kibernetika. No. 3, 64–67 (1982).
D. K. Faddeev and V. N. Faddeeva, Computational Methods of Linear Algebra, Freeman, San Francisco (1963).
A. N. Kolmogorov and S. Fomin, Elements of the Theory of Functions and Functional Analysis [in Russian], Nauka, Moscow (1976).
“Development of a vector matrix processor with a high degree of parallelism of operations in the basis of the microprocessors,” Report on Scientific Research, Institute of Cybernetics of the Academy of Sciences of the Ukrainian SSR, directed by Z. L. Rabinovich, GR 79048224; Inv. No. 02821033980, Kiev (1982).
N. S. Bakhvalov, Numerical Methods, Vol. I [in Russian], Nauka, Moscow (1975).
I. S. Berezin and N. G. Zhidkov, Computing Methods, Vol. I [in Russian], Nauka, Moscow (1970).
I. S. Berezin and N. G. Zhidkov, Computing Methods, Vol. II, [in Russian], Nauka, Moscow (1962).
O. N. P'yavchenko and Ya. E. Romm, “A modification of the tabular-interpolation method for the computation of elementary functions on a computer” in: Design Problems and the Application of Discrete Systems in Control. Abstracts of Communications, I, Internat. Conference of Young Scientists, Minsk (1977)-VINITI, Lyubertsy (1977), pp. 326–328.
Additional information
Translated from Kibernetika, No. 2, pp. 19–26, March–April, 1988.
Rights and permissions
About this article
Cite this article
Surzhenko, I.F., Romm, Y.E. Machine error of parallel algorithms. Cybern Syst Anal 24, 160–170 (1988). https://doi.org/10.1007/BF01082604
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01082604