Cluster-Based Distributed Algorithms for Very Large Linear Equations

作     者：古志民 MARTA Kwiatkowska 付引霞 

作者机构：School of Computer Science and Technology Beijing Institute of Technology Beijing 100081 China School of Computer Science University of Birmingham Birmingham B15 2TT United Kingdom 

出 版 物：《Journal of Beijing Institute of Technology》 (北京理工大学学报（英文版）)

年 卷 期：2006年第15卷第1期

页      面：66-70页

核心收录：

学科分类：0810[工学-信息与通信工程] 08[工学] 0805[工学-材料科学与工程（可授工学、理学学位）] 0812[工学-计算机科学与技术（可授工学、理学学位）] 081202[工学-计算机软件与理论] 

基　　金：StudyAbroadFoundationofChina(21307D05) theBasicResearchFoundationofBeijingInstituteofTechnology(0301F18) 

主　　题：Gaussian elimination partition cluster-based distributed computing 

摘      要：In many applications such as computational fluid dynamics and weather prediction, as well as image processing and state of Markov chain etc., the grade of matrix n is often very large, and any serial algorithm cannot solve the problems. A distributed cluster-based solution for very large linear equations is discussed, it includes the definitions of notations, partition of matrix, communication mechanism, and a master-slaver algorithm etc., the computing cost is O（n^3/N）, the memory cost is O（n^2/N）, the I/O cost is O（n^2/N）, and the com- munication cost is O（Nn ）, here, N is the number of computing nodes or processes. Some tests show that the solution could solve the double type of matrix under 10^6 × 10^6 effectively.