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 long ago 35 years. The dominant consider this improvement used to be the improvement in computing device expertise. machine parameters have been systematically enhanced via electron tubes, transistors and built-in circuits of ever-increasing integration density, which additionally motivated the advance of latest algorithms and programming tools. a few years in the past the location in desktops improvement used to be that no extra enhancement in their functionality will be accomplished by means of expanding the rate in their logical components, end result of the actual barrier of the utmost move pace of electrical indications. one other enhancement of laptop functionality has been accomplished through parallelism, which makes it attainable by way of an appropriate association of n processors to acquire a practice ance raise of as much as n instances. study into parallel computations has been performed for a number of years in lots of nations and lots of result of basic significance were bought. Many parallel desktops were designed and their algorithmic and application ming platforms outfitted. Such pcs comprise ILLIAC IV, DAP, STARAN, OMEN, STAR-100, TEXAS tools ASC, CRAY-1, C mmp, CM*, CLIP-3, PEPE. This pattern is supported by way 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) higher and bigger calls for for pace and reliability of desktops are made.

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Multiplication of n matrices is given for k = n 2 , n 3 , n 4 , with the maximum value of Sk/Ck occurring with k = n 3 • REFERENCES [I] BoRODIN, A. : The Computational Complexity of Algebraic and Numeric Problems. American Elsevier, New York, 1975. [2] BRENT, R. : The parallel evaluation of arithmetic expressions in logarithmic time. 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.

18] TRAUB, J. : Parallel algorithms and parallel computational complexity. Proc. IFIP Congress. North-Holland Pub!. , Amsterdam, 1974, pp. 685--687. Appendix A PARALLEL ALGORITHM FOR SOLVING BAND SYSTEMS AND MATRIX INVERSION 1. Introduction. Recently, several studies have appeared about the solution of systems of linear equations Ax = b on parallel computers, where A is a real n by n dense, triangular or tridiagonal matrix (1-6]. g. a band structure with non-scalar constant coefficients, although there are studies of this for serial computers.

Single components of the solution are iterated on different processors in a random order, as global variables stored in a memory shared by all processors. The iterative process ends when a certain condition is satisfied which is controlled by a processor reserved for it. To ensure the convergence of this scheme, the succession of iterations is restricted in that there must exist a fixed postive integer s, so that in the execution of the i-th iteration of some component it is possible to use a component of the j-th iteration only if j ~ i - s, and it is necessary that in an execution of the algorithm each component of the solution is iterated for "infinitely many" times.

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

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