Abstract
Implementation of various numerical methods often needs organisation of computation using complex iterative formulae, i.e. cycles. The time for performing a program on a computer and the necessary storage capacity are largely dependent on form of these formulae. It is desirable to construct computations so that each iterative step might use the results obtained at the previous steps as completely as possible. This implies the association of the given formulae with the recurrent relations, that bring about the same result but economise the arithmetic operations. A special algebraic method has been created that provides for the automatic construction of such recurrent relations. This method and main ways of its use in the algorithms of cycle optimisation, in the computer algebra systems and in algorithms of automatic parallel programs construction are explained. Many examples and programs are given.
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References
Zima E.V., Automatic Construction of Systems of Recurrence Relations. (in Journal of Computational Mathematics and Mathematical Physics.), Vol. 24, N 6, (1984), pp. 193–197.
Zima E.V., Transformations of Expressions Associated with Systems of Recursion Relations. (Moscow University Computational Mathematics and Cybernetics, 1985, N 1, pp. 60–66.)
Aho A.V., Ullman J.D., The theory of parsing, translation and compiling. Vol. 2: Compiling. (Prentice-Hall, Inc. Englewood Cliffs, N.J. 1973)
Hockney R.W., Jesshope C.R. Parallel Computers: arhitecture, programming and algorithms. Aden Hilgen Ltd., Bristol, 1983.
Evans, D.J.(ed.), Parallel Processing Systems. (Cambridge University press, 1982).
Supercomputers. Class YI Systems, Hardware and Software. S.Fernbach (ed.), North-Holland, 1986.
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© 1993 Springer-Verlag Berlin Heidelberg
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Zima, E.V. (1993). Recurrent relations and speed-up of computations using computer algebra systems. In: Fitch, J. (eds) Design and Implementation of Symbolic Computation Systems. DISCO 1992. Lecture Notes in Computer Science, vol 721. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-57272-4_32
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DOI: https://doi.org/10.1007/3-540-57272-4_32
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