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(n3/N), the memory cost is O(n2/N), the I/O cost is O(n2/N), and the communication 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 106×106 effectively.
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.
基金
StudyAbroadFoundationofChina(21307D05)
theBasicResearchFoundationofBeijingInstituteofTechnology(0301F18)
