Mathematical Foundations of Parallel Computing

Mathematical Foundations of Parallel Computing

Valentin V. Voevodin

Language: English

Pages: 362

ISBN: 2:00362151

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.

Robot Motion and Control: Recent Developments (Lecture Notes in Control and Information Sciences)

Todd Lammle's CCNA/CCENT IOS Commands Survival Guide: Exams 100-101, 200-101, and 200-120

Multidimensional Particle Swarm Optimization for Machine Learning and Pattern Recognition

Internetworking with TCP/IP, Volume 1: Principles, Protocols, and Architecture (6th Edition)

Software Architecture: A Comprehensive Framework and Guide for Practitioners

Gems of Theoretical Computer Science

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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

inequality vectors s° s s holds. does n o t c o n t a i n with initial zero t h e schedule vector conditions initial 01s). s . Consequently, vector conditions We have any c l a s s c a n be g e n e r a t e d vector already by a noted ft^ls) from "parallel that In t h e "zero i t c a n a l w a y s be a d d e d t o t h a t s e t . T h e i n e q u a l i t y 0 £ s good f o r any n o n n e g a t i v e ft ( 0 ) 01s) using the vector holds with the class translation"

b y t h e 2 be n / 2 (we w r i t e execution o f l e n g t h 2 . The o n l y ex- t h e nodes w i t h t h e g r a p h may w e l l r e m o v a l o f some a r c s , r e s u l t e d would by paths time T h u s we h a v e would lost i n t h e g r a p h whose c r i t i c a l t h e most s i g n i f i c a n t accordingly a l l parallelism term be o f t h e same path length only). The a l g o r i t h m order o f magnitude. by t h e u n f o r t u n a t e expansion o f the graph.

f the Therefore t h e number a l l such o farcs i n it. It ted i s i m p o r t a n t t o have v a r i o u s c r i t e r i a cuts ( i f any) a g i v e n a l g o r i t h m graph t o determine admits. what One o f t h e s e direci s pro- cured by STATEMENT 1 4 . 3 . (z , P the w ) with P pairs of distinct node. vector Then with z , i nonzero Suppose l p at ion requires at under the schedule corresponding least linking possess a to a p words of delay

algorithm. Suppose that we managed to find such e' s a t i s f y i n g (20.2) that .ft c n = 0 . The c o m p u t a t i o n quently, u computed s e n t e d as f o l l o w s : (20.2) i s exact i n t h e presence f o rperturbed o f roundoff input errors data. Conse- may b e repre- 179 u If the equivalent is the r e s u l t of ly perturbed Now large uation the data, in ^ lent perturbations (17.2). I f the rors t h e n no other influence quence can (17.2)

Download sample

Download