Mathematical Foundations of Parallel Computing
Valentin V. Voevodin
Format: PDF / Kindle (mobi) / ePub
Parallel implementation of algorithms involves many difficult problems. In particular among them are round-off analysis, the way to convert sequential programmes and algorithms into parallel mode, the choice of appropriate or optimal computer architect and so on. To solve the stumbling blocks of these problems it is necessary to know the structure of algorithms very well. The book treats the mathematical mechanism that permits us to investigate structures of both sequential and parallel algorithms. This mechanism allows us to recognize and explain the relations between different methods of constructing parallel algorithms, methods to analyze round-off errors, methods to optimize memory traffic, methods to work out the fastest implementation for a given parallel computer and other methods attending the joint investigation of algorithms and computers.
I s a c c o m p l i s h e d . The r e s u l t i n g More i s preserved, t h e a t which moment o f Take any e n u m e r a t i o n o f time vector t h e development o f e x e c u t i o n i s r u n time. or a hypothetical a t which the i t h t - ( t ^ t ^ , ...) i s every actual or hypothetical algorithm t itself s y s t e m , we later. o f algorithm implementation unavoidably used o f algorithms coordinate properties of algorithms. be d i s c u s s e d designed computer,.
Number o f help studied rithm, we can cope with solution abstract parallel the set readily algorithms, parallel us algorithm the processors, Having various to makes their of the to the task. problem machine, types, The latter that since and the implementations proceed i . e . use of abs- parallel t o i n t r o d u c e such a machine. i n w h i c h way graph inter- that differ. quite ab- i t has needed use same the for- operation must u n d.
A n d n e e d some sufficiently storage equipment, and data These a s s u m p t i o n s a r e , large in a elaboration. data storage devices do than t h e average time required t o perform pacity i s 1lmited. That I s why i s t o be t a k e n i f we s t r i v e Existing kinds. computer These d e v i c e s gorithms systems possess channels. efficiently the limitations cated incorporate storage o f memory computer devices varying characteristics algo- of.
Algorithms. But what should the goal t o be used i s of special utilitarian algorithms. us f o rinquiry, the mathematical apparatus paramount this plan into Importance. effect will I n the f i r s t description of the class o f algorithms possibility t o construct a allow place, us t o s o l v e we w i l l t h a t we s t u d y . mathematical apparatus two problems obtain This the exact opens up t h e t o explore their 2 structures. to As we analyze place,.
At < % t h e f u n c t i o n s F^ t o do (19.1) i coordinate vector. amount o f a r i t h m e t i c (19,1) we of relations k concurrently, a l lpartial computed a l o n g w i t h sary information tradiimplic- grad u 1 and the i s ' p