By Jozef Mikloško, Vadim Evgenich Kotov (auth.), Jozef Mikloško, Vadim Evgenich Kotov (eds.)

ISBN-10: 3662111063

ISBN-13: 9783662111062

ISBN-10: 366211108X

ISBN-13: 9783662111086

Both algorithms and the software program . and of computerized desktops have passed through a fast improvement some time past 35 years. The dominant think about this improvement used to be the development in computing device know-how. computing device parameters have been systematically enhanced via electron tubes, transistors and built-in circuits of ever-increasing integration density, which additionally stimulated the advance of latest algorithms and programming tools. a few years in the past the placement in pcs improvement was once that no extra enhancement in their functionality can be completed by means of expanding the rate in their logical components, as a result of actual barrier of the utmost move pace of electrical indications. one other enhancement of desktop functionality has been accomplished via parallelism, which makes it attainable through an appropriate association of n processors to procure a practice­ ance raise of as much as n instances. learn into parallel computations has been performed for a number of years in lots of nations and plenty of result of basic significance were got. Many parallel pcs were designed and their algorithmic and software­ ming platforms equipped. Such pcs contain ILLIAC IV, DAP, STARAN, OMEN, STAR-100, TEXAS tools ASC, CRAY-1, C mmp, CM*, CLIP-3, PEPE. This development is supported by means of the truth that: a) many algorithms and courses are hugely parallel of their constitution, b) the hot LSI and VLSI applied sciences have allowed processors to be mixed into huge parallel buildings, c) larger and larger calls for for velocity and reliability of pcs are made.

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18, 1974, 138-148. [14] KucK, D. : Parallel processing of ordinary programs. Advances in Computers, Vol. 15. Academic Press, New York, 1977, pp. 119>---179. [15] MIRANKER, W. K. and LINIGER, W. : Parallel methods for the numerical integration of ordinary differential equations. Math. , 21, 1967, 304-320. : Parallelism exposure and exploitation in programs. Tech. Report No. 71-424. Comp. Sci. , Univ. of Illinois, 1971. : Parallel methods for integrating ordinary differential equations. Comm. ACM, 7, 1964, 737-743.

Proc. Complexity of Sequential and Parallel Numerical Algorithms. J. F. Traub (Editor). Academic Press, New York, 1973, pp. 83-102. [3] BRENT, R. : The parallel evaluation of general arithmetic expression. J. ACM, 21, 1974, 201--206. : Fast parallel matrix inversion algorithms. Tech. Report, Univ. of California, Berkeley, 1974. : On the parallel complexity of some computational problems. Dissertation. Univ. of California, Berkeley, 1974. EMAN, W. : Some complexity results for matrix computations on parallel processors.

Hence, the asymptotic number of iterations is also O(n 112 log n), if optimal w and (j = O(n- 2 ) are assumed for the process (9). In order to satisfy the criterion (8) with (j > 0 for the iterative process (9), the new criterion is [10] The semidirect process (7) can be replaced by the process (9) without increasing the asymptotic number of iterations. Moreover, this substitution makes it possible to achieve new complexity estimates for the parallel computation of one iteration. However, the double solution of the discrete Poisson equations, required in (3), is held in the vector oCk+O.

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Algorithms, Software and Hardware of Parallel Computers by Jozef Mikloško, Vadim Evgenich Kotov (auth.), Jozef Mikloško, Vadim Evgenich Kotov (eds.)

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