Abstract
A general technological scheme for constructing an algorithm used to calculate an approximate solution to a problem with certain initial data, set constraints for an approximate solution error and computation time under limited computation resources are considered in the paper.
Similar content being viewed by others
REFERENCES
V. V. Ivanov, M. D. Babich, A. I. Berezovskii, P. N. Besarab, V. K. Zadiraka, and V. A. Lyudvichenko, “Characteristics of problems, algorithms, and computers in program systems of computational mathematics,” Preprint AN USSR, V. M. Glushkov Inst. Cybern., 84-36 (1984).
D. J. Evans (ed.), Parallel Processing Systems [Russian translation], Mir, Moscow (1985).
V. B. Kotov and J. Mikloshko (eds.), Algorithms, Software, and Architecture of Multiprocessor Systems [in Russian], Nauka, Moscow (1982).
V. V. Ivanov, Methods of Computer Calculations: A Handbook [in Russian], Naukova Dumka, Kiev (1986).
I. V. Sergienko, V. K. Zadiraka, M. D. Babich, A. I. Berezovskii, P. N. Besarab, and V. A. Lyudvichenko, “Methods of constructing T-efficient algorithms for calculating e-solutions to problems of computing and applied mathematics,” in: Theory of Calculations [in Ukrainian], V. M. Glushkov Institute of Cybernetics, NAS Ukr., Kiev (1999), pp. 325-330.
M. D. Babich, A. I. Berezovskii, P. N. Besarab, V. K. Zadiraka, V. A. Lyudvichenko, and I. V. Sergienko, “T-efficient calculation of the e-solutions to problems of calculation and applied mathematics. Pts. I, II,” Kibern. Sist. Analiz, No. 2, 49-70; No. 3, 97-118 (2001).
E. Hairer, S. Norsett, and G. Wanner, Solving Ordinary Differential Equations. Nonstiff Problems [Russian translation], Mir, Moscow (1990).
V. V. Voevodin, Mathematical Models and Methods in Parallel Processes [in Russian], Nauka, Moscow (1986).
G. Rodrigue (ed.), Parallel Computations [Russian translation], Mir, Moscow (1985).
J. Ortega, Introduction to Parallel and Vector Solution of Linear Systems [Russian translation], Mir, Moscow (1991).
V. M. Glushkov, Yu. V. Kapitonova, and A. A. Letichevskii, “An approach to realization of parallel calculations in multiprocessor computing systems,” in: Parallel Programming and Computing Systems [in Russian], Issue 1, Novosibirsk (1980), pp 3-25.
L. D. Elfimova and Yu. V. Kapitonova, “A fast algorithm for matrix multiplication and its efficient realization on systolic arrays,” Kibern. Sist. Analiz, No. 1, 135-150 (2001).
N. N. Mirenkov, Parallel Programming for Multimodular Computing Systems [in Russian], Radio i Svyaz', Moscow (1989).
I. Ya. Akushskii and D. I. Yuditskii, Machine Arithmetic in Residue Classes [in Russian], Sov. Radio, Moscow (1968).
J. G. McClelland and C. M. Rader, Application of the Number Theory in Digital Signals Processing [Russian translation], Radio i Svyaz', Moscow (1983).
V. K. Zadiraka and S. S. Mel'nikova, Digital Signal Processing [in Russian], Naukova Dumka, Kiev (1993).
V. K. Zadiraka and O. S. Oleksyuk, Methods of Protecting Financial Information [in Ukrainian], Vyshcha Shkola, Kiev (2000).
A. Kitaev, A. Shen', and M. Vyalyi, Classical and Quantum Calculations [in Russian], MTsNMO, Moscow (1999).
C. Pomerance, “The number field sieve,” Mathematics of Computation 1943-1993; A Half-Century of Computational Mathematics, Amer. Math. Soc., 465-480 (1994).
R. L. Rivest, A. Shamir, and L. Adleman, “A method for obtaining digital signatures and public-key cryptosystems,” Commun. ACM, Mach. 21, No. 2, 120-126 (1978).
P. Shor, “Algorithms for quantum computation: discrete logarithms and factoring,” Proc. 35th Annual Symposium on Foundations of Computer Science, IEEE Computer Society Press (1994), pp. 124-134.
D. Boneh and R. J. Lipton, “Quantum cryptanalysis of hidden linear functions,” Lect. Notes Comput. Sci., No. 963, 424-437 (1995).
R. Beals, “Quantum computation of Fourier transforms over symmetricgroups,” Proc. 29th Ann. ACM Symp. On Theory of Comput., El Paso, USA, 4-6 May, 1997, El Paso (1997), pp. 48-53.
D. Deutsch, “Quantum theory, the Church-Turing principle and the universal quantum computer,” Proc. R. Soc. Lond, Vol. A 400 (1985), p. 97.
A. C.-C. Yao, “Quantum circuit complexity,” FOCS'34 (1993), p. 352.
X. Gibbs, Optical Bistability. Light Control Using Light [Russian translation], Mir, Moscow (1988).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Sergienko, I.V., Zadiraka, V.K., Babich, M.D. et al. Computer Technology of Constructing T-Efficient Algorithms for Computing ε-Solutions of Computational and Applied Mathematical Problems. Cybernetics and Systems Analysis 38, 837–845 (2002). https://doi.org/10.1023/A:1022987803904
Issue Date:
DOI: https://doi.org/10.1023/A:1022987803904