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Optimization of computations

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References

  1. A. A. Dorodnitsyn, “Computational mathematics”, in: Encyclopedia of Cybernetics [in Russian], Vol. 1 (1974), pp. 201–202.

  2. L. V. Kantorovich and G. P. Akilov, Functional Analysis in Normed Spaces [in Russian], Fizmatgiz, Moscow (1959).

    Google Scholar 

  3. M. A. Krasnosel'skii, G. M. Vainikko, P. M. Zabreiko, et al., Approximate Solution of Operator Equations [in Russian], Nauka, Moscow (1969).

    Google Scholar 

  4. A. N. Tikhonov and A. D. Gorbunov, “Error estimate of Runge-Kutta type methods and choice of optimal grids”, Zh. Vychisl. Mat. Mat. Fiz.,4, No. 2, 232–241 (1964).

    Google Scholar 

  5. V. M. Glushkov, An Introduction to Cybernetics [in Russian], Izd. AN UkrSSR, Kiev (1964).

    Google Scholar 

  6. V. S. Mikhalevich, “Sequential optimization algorithms and their application, part I”, Kibernetika, No. 1, 45–55 (1965).

    MATH  Google Scholar 

  7. V. S. Mikhalevich, “Sequential optimization algorithms and their application, part II”, Kibernetika, No. 2, 5–89 (1965).

    MATH  Google Scholar 

  8. V. V. Voevodin, Rounding Error and Stability in Direct Methods of Linear Algebra [in Russian], VTs MGU, Moscow (1969).

    Google Scholar 

  9. G. I. Marchuk and V. I. Lebedev, Numerical Methods in Neutron Transport Theory [in Russian], Atomizdat, Moscow (1971).

    Google Scholar 

  10. A. A. Samarskii, An Introduction to the Theory of Difference Schemes [in Russian], Nauka, Moscow (1971).

    Google Scholar 

  11. V. V. Ivanov, “Some topics of optimization of computations”, in: Computer Software [in Russian], Inst. Kibern. AN UkrSSR, Kiev (1972), pp. 149–172.

    Google Scholar 

  12. N. S. Bakhvalov, Numerical Methods [in Russian], Nauka, Moscow (1973).

    Google Scholar 

  13. P. I. Bondarchuk and V. Ya. Skorobogat'ko, Branching Continuous Fractions and Their Applications [in Ukrainian], Naukova Dumka, Kiev (1974).

    Google Scholar 

  14. I. I. Lyashko, V. L. Makarov, and A. A. Skorobogat'ko, Computational Methods (Numerical Analysis, Methods of Solution of Problems of Mathematical Physics) [in Russian], Vishcha Shkola, Kiev (1977).

    Google Scholar 

  15. N. P. Korneichuk, Extremal Problems of Approximation Theory [in Russian], Nauka, Moscow (1976).

    Google Scholar 

  16. V. K. Dzyadyk, An Introduction to the Theory of Uniform Approximation of Functions by Polynomials [in Russian], Nauka, Moscow (1977).

    Google Scholar 

  17. A. N. Tikhonov and V. Ya. Arsenin, Methods of Solution of Ill-Posed Problems [in Russian], Nauka, Moscow (1974).

    Google Scholar 

  18. V. A. Morozov, Regular Methods of Solution of Ill-Posed Problems [in Russian], Izd. MGU, Moscow (1974).

    Google Scholar 

  19. I. V. Sergienko and V. V. Skopetskii, “Analysis of data processing systems and issues of increasing their efficiency”, Kibernetika, No. 6, 61–72 (1977).

    Google Scholar 

  20. A. Yu. Luchka, Projection-Iterative Methods for Solving Integral and Differential Equations [in Russian], Naukova Dumka, Kiev (1980).

    Google Scholar 

  21. V. K. Zadiraka, Theory of Evaluation of the Fourier Transform [in Russian], Naukova Dumka, Kiev (1983).

    Google Scholar 

  22. V. M. Glushkov, V. V. Ivanov, V. S. Mikhalevich et al., Reserves for Optimization of Computations [in Russian], Preprint 77-67, Inst. Kibern. AN UkrSSR, Kiev (1977).

    Google Scholar 

  23. V. V. Ivanov, M. D. Babich, A. I. Berezovskii, et al., Characteristics of Problems, Algorithms, and Computers in Software Systems for Computational Mathematics [in Russian], Preprint 84-36, Inst. Kibern. AN UkrSSR, Kiev (1984).

    Google Scholar 

  24. V. V. Ivanov, Computer Computational Methods: A Handbook [in Russian], Naukova Dumka, Kiev (1986).

    Google Scholar 

  25. V. V. Ivanov, M. D. Babich, A. I. Berezovskii, et al., “Software system POM-1 for solving some classes of problems of computational mathematics”, Upr. Sist. Mash., No. 2, 105–109 (1986).

    Google Scholar 

  26. V. M. Glushkov, “An interactive method for solving optimization problems”, Kibernetika, No. 4, 2–7 (1975).

    MATH  Google Scholar 

  27. V. S. Mikhalevich and V. L. Volkovich, Computational Methods for Complex System Analysis and Design [in Russian], Nauka, Moscow (1982).

    Google Scholar 

  28. V. S. Mikhalevich, I. V. Sergienko, and N. Z. Shor, “Analysis of solution methods of optimization problems and their applications”, Kibernetika, No. 4, 89–113 (1981).

    MathSciNet  Google Scholar 

  29. I. V. Sergienko, Mathematical Models and Methods of Solution of Discrete Optimization Problems [in Russian], Naukova Dumka, Kiev (1988).

    Google Scholar 

  30. N. Z. Shor, Minimization Methods for Nondifferentiable Functions and Their Applications [in Russian], Naukova Dumka, Kiev (1979).

    Google Scholar 

  31. I. I. Eremin and N. N. Astaf'ev, An Introduction to Linear and Convex Programming Theory [in Russian], Nauka, Moscow (1976).

    Google Scholar 

  32. V. S. Mikhalevich and N. Z. Shor, Numerical Solution of Multi-Alternative Problems by the Method of Sequential Analysis of Alternatives [in Russian], Part 1 (1962).

  33. V. S. Mikhalevich (ed.), Computational Methods for Optimal Design Decisions [in Russian], Naukova Dumka, Kiev (1977).

    Google Scholar 

  34. D. B. Yudin, and A. S. Nemirovskii, “Information complexity and efficient methods for solving convex extremal problems”, Ékon. Mat. Metody,12, No. 3, 367–369 (1976).

    Google Scholar 

  35. N. Z. Shor, “Structure of algorithms for numerical solution of optimal scheduling and design problems”, Abstract of thesis [in Russian], Kiev (1964).

  36. N. Z. Shor, “Using the space stretching operation for minimization of convex functions”, Kibernetika, No. 1, 6–12 (1970).

    MATH  Google Scholar 

  37. N. Z. Shor and N. G. Zhurbenko, “Minimization method with space stretching in the direction of the difference of two successive gradients”, Kibernetika, No. 3, 51–69 (1971).

    Google Scholar 

  38. N. Z. Shor and V. I. Gershovich, “Family of algorithms for solving convex programming problems”, Kibernetika, No. 4, 62–76 (1979).

    MathSciNet  Google Scholar 

  39. L. G. Khachiyan, “Polynomial-time linear programming algorithm”, Dokl. Akad. Nauk SSSR,244, No. 5, 1089–1096 (1979).

    MathSciNet  Google Scholar 

  40. M. K. Kozlov, L. G. Khachiyan, and S. P. Tarasov, “Polynomial solvability of convex quadratic programming”, Zh. Vychisl. Mat. Mat. Fiz.,20, No. 5, 1319–1323 (1980).

    MathSciNet  Google Scholar 

  41. M. Grotschel, I. Lovasz, and A. Schrijver, Geometric Algorithms and Combinatorial Optimization, Springer, Berlin (1988).

    Google Scholar 

  42. I. I. Érlikh, S. P. Tarasov, and L. G. Khachiyan, “Inscribed ellipsoid method”, Dokl. Akad. Nauk SSSR,293, No. 5, 1081–1085 (1988).

    Google Scholar 

  43. N. Z. Shor and O. A. Berezovsky, “New algorithms for constructing ellipsoids”, Optim. Methods Software,1, 283–299 (1992).

    Google Scholar 

  44. V. S. Mikhalevich, V. A. Trubin, and N. Z. Shor, Mathematical Methods for Production-Transportation Scheduling Problems [in Russian], Nauka, Moscow (1986).

    Google Scholar 

  45. M. R. Garey and D. S. Johnson, Computers and Intractability, Freeman, San Francisco (1979).

    Google Scholar 

  46. W. H. Cunningham, “Optimal attack and reinforcement of a network”, J. ACM,32, 549–561 (1985).

    Article  MATH  MathSciNet  Google Scholar 

  47. V. A. Trubin, “Network strength, reinforcement, and tree packing”, Kibernetika, No. 2, 67–75 (1991).

    MATH  MathSciNet  Google Scholar 

  48. G. Gallo, M. D. Grigoriadis, and R. E. Tarjan, “A fast parametric maximum flow algorithm and applications”, SIAM J. Comput.,18, No. 1, 30–55 (1989).

    MathSciNet  Google Scholar 

  49. V. A. Trubin, “The strength of a graph and packing of trees and branches”, Kibern. Sist. Analiz, No. 3, 95–99 (1993).

    Google Scholar 

  50. P. A. Pevzner, “An efficient packing algorithm for branches in a weighted graph”, in: Combinatorial Methods in Flow Problems [in Russian], No. 3 (1979), pp. 113–123.

  51. B. N. Pshenichnyi, Linearization Method [in Russian], Nauka, Moscow (1983).

    Google Scholar 

  52. V. M. Glushkov, Yu. V. Kapitonova, and A. A. Letichevskii, “Theory of data structures and synchronous parallel computation”, Kibernetika, No. 6, 2–15 (1976).

    Google Scholar 

  53. V. V. Voevodin, Mathematical Models and Methods in Parallel Processes [in Russian], Nauka, Moscow (1986).

    Google Scholar 

  54. V. S. Mikhalevich and I. N. Molchanov, Supercomputer Development Trends and Resulting Problems [in Russian], Preprint 84-4, Inst. Kibern. AN UkrSSR, Kiev (1984).

    Google Scholar 

  55. V. N. Faddeeva and D. K. Faddeev, “Parallel computations in linear algebra, parts 1, 2”, Kibernetika, No. 6, 28–40 (1977); No. 3, 18–31 (1982).

    MathSciNet  Google Scholar 

  56. V. M. Glushkov, “Efficiency estimates of complex systems and organization of complex processes”, in: Computer Software [in Russian], Inst. Kibern. AN UkrSSR, Kiev (1972), pp. 3–17.

    Google Scholar 

  57. I. V. Sergienko, Methods of Organization of Computational Process on Computers [in Russian], Inst. Kibern. AN UkrSSR, Kiev (1971).

    Google Scholar 

  58. Yu. V. Kapitonova, “Issues of organization of special-purpose software systems”, in: Computer Software [in Russian], Inst. Kibern. AN UkrSSR, Kiev (1972), pp. 252–254.

    Google Scholar 

  59. M. D. Babich, “An approximation-iteration method for solving nonlinear operator equations”, Kibernetika, No. 1, 21–28 (1991).

    MATH  MathSciNet  Google Scholar 

  60. M. D. Babich and L. B. Shevchuk, “An algorithm for approximate solution of systems of nonlinear equations”, Kibernetika, No. 2, 74–79 (1982).

    Google Scholar 

  61. S. M. Nikol'skii, Quadrature Formulas [in Russian], Nauka, Moscow (1974).

    Google Scholar 

  62. N. S. Bakhvalov, “On properties of optimal methods of solution of problems of mathematical physics”, Zh. Vychisl. Mat. Mat. Fiz.,10, No. 3, 555–568 (1970).

    MATH  Google Scholar 

  63. Optimization of Computations [in Russian], Nos. 1–3, Inst. Kibern. AN UkrSSR, Kiev (1977).

  64. V. K. Zadiraka and S. S. Mel'nikova, Digital Signal Processing [in Russian], Naukova Dumka, Kiev (1993).

    Google Scholar 

  65. V. S. Mikhalevich, I. V. Sergienko, V. K. Zadiraka, et al., Developing a Software Quality Testing System [in Russian], Kiev (1989). Unpublished manuscript VNTNTs No. 029.0.037707.

  66. J. W. Cooley and J. W. Tukey, “An algorithm for the machine calculation of complex Fourier series”, J. Math. Comput., No. 5, 257–301 (1965).

    MathSciNet  Google Scholar 

  67. J. H. McClellan and C. M. Rader, Number Theory in Digital Signal Processing, Prentice-Hall, Englewood Cliffs, NJ (1979).

    Google Scholar 

  68. V. M. Glushkov, Yu. V. Kapitonova, and A. A. Letichevskii, “Macropipelined computations on data structures”, Kibernetika, No. 4, 13–21 (1981).

    MathSciNet  Google Scholar 

  69. V. M. Glushkov and I. N. Molchanov, “On some problems of solving problems on computers with parallel organization of computations”, Kibernetika, No. 4, 82–88 (1981).

    Google Scholar 

  70. S. S. Agayan and D. Z. Gevorkyan, “Complexity and parallel algorithms for discrete orthogonal transformations”, Kibern. Vychisl. Tekhn., No. 4, 124–169 (1988).

    MathSciNet  Google Scholar 

  71. P. N. Besarab, “On speed of parallel algorithms for numerical integration of ordinary differential equations”, Abstracts of papers at 1st All-Union Conf. on Homogeneous Computing Media and Systolic Structures [in Russian], L'vov (1990), pp. 18–24.

  72. Yu. G. Evtushenko, Methods of Solution of Extremal Problems and Their Application in Optimization Systems [in Russian], Nauka, Moscow (1982).

    Google Scholar 

  73. M. D. Babich and L. B. Shevchuk, “On approximate solution of some classes of extremal problems”, in: Numerical Methods and Software Package Development Technology [in Russian], Inst. Kibern. AN UkrSSR, Kiev (1990), pp. 56–61.

    Google Scholar 

  74. V. K. Zadiraka and E. A. Melekhina, “On computer implementation of efficient algorithms for calculating discrete convolution”, Kibernetika, No. 1, 129–139 (1994).

    Google Scholar 

  75. V. K. Zadiraka, O. S. Kondratenko, V. A. Lyudvichenko, and Ya. B. Malanyuk, “On interactive control programs in software packages for solving problems of computational mathematics with prescribed quality characteristics”, Upr. Sist. Mash., No. 2, 39–44 (1993).

    Google Scholar 

  76. J. F. Traub and H. Wozniakowski, A General Theory of Optimal Algorithms [Russian translation], Mir, Moscow (1983).

    Google Scholar 

  77. J. F. Traub, G. Vasilovski, and H. Wozniakowski, Information, Uncertainty, Complexity [Russian translation], Mir, Moscow (1988).

    Google Scholar 

  78. D. Knuth, The Art of Computer Programming [Russian translation], Vol. 2, Mir, Moscow (1977).

    Google Scholar 

  79. V. S. Mikhalevich, I. V. Sergienko, V. K. Zadiraka, et al., Issues in Optimization of Computations [in Ukrainian], Preprint 99-13, Inst. Kibern. im. V. M. Glushkov, Kiev (1993).

    Google Scholar 

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Translated from Kibernetika i Sistemnyi Analiz, No. 2, pp. 65–94, March–April, 1994.

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Mikhalevich, V.S., Sergienko, I.V., Zadiraka, V.K. et al. Optimization of computations. Cybern Syst Anal 30, 213–235 (1994). https://doi.org/10.1007/BF02366426

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