Cluster-Based Distributed Algorithms for Very Large Linear Equations

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.