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

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

Both algorithms and the software program . and of automated pcs have passed through a speedy improvement long ago 35 years. The dominant think about this improvement was once the improvement in laptop expertise. computing device parameters have been systematically better via electron tubes, transistors and built-in circuits of ever-increasing integration density, which additionally prompted the improvement of recent algorithms and programming equipment. a few years in the past the location in desktops improvement was once that no extra enhancement in their functionality will be completed via expanding the rate in their logical parts, as a result of the actual barrier of the utmost move velocity of electrical signs. one other enhancement of machine functionality has been accomplished by means of parallelism, which makes it attainable by way of an appropriate association of n processors to acquire a practice­ ance elevate of as much as n occasions. examine into parallel computations has been conducted for a number of years in lots of nations and plenty of result of basic significance were received. Many parallel desktops were designed and their algorithmic and application­ ming structures equipped. Such desktops contain ILLIAC IV, DAP, STARAN, OMEN, STAR-100, TEXAS tools ASC, CRAY-1, C mmp, CM*, CLIP-3, PEPE. This pattern is supported by means of the truth that: a) many algorithms and courses are hugely parallel of their constitution, b) the recent LSI and VLSI applied sciences have allowed processors to be mixed into huge parallel constructions, c) better and bigger calls for for velocity and reliability of pcs are made.

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The results are also described, and it follows from these that data transfer between processors may be the limiting factor in the effectiveness of parallel computations. In the fourth and last part, the speedup of parallel algorithms is defined and related theoretical results are explained using linear and non-linear recurrent relations as examples. In conclusion, the possibility of comparing an a priori selection of suitable parallel algorithms is explained. 1 Parallel computation of xn Investigation into the complexity of parallel algorithms brings new ideas and surprising results.

IX compute x}il = gi - rix}~/l, j odd, x}il = gi- rixj2~, j even and < n. The approximate solution of the system Ax= cis xoxl. The values ID, IF and IX can be a priori established to the desired accuracy or computed. , I I q= 1 + Vl="):. Let II II denote infinite norm. llx

Although quite satisfactory from the point of view of algebraic complexity, like many shooting methods, also this algorithm suffers from an exponential growth in roundoff error and from the possibility of over-or underflow. These drawbacks are due to the parallel algorithm for solving lower band triangular systems (6).

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