DESIGN AND ANALYSIS OF MPI PARALLEL ALGORITHM FOR
LARGE-SCALE MATRIX INVERSION
1)School of Geodesy and Geomatics,Wuhan University,Wuhan 430079
2)Key Lab of Geospace Environment and Geodesy,Ministry of Education,Wuhan University,Wuhan 430079
Abstract:In order to solve the problem in large scale matrix inversion with least square solving,the parallel algorithm to inverse the highorder dense symmetrical positive define matrix with GaussJordan method on the basis of MPI was proposed.Considering the high memory demand on single processor for this algorithm,the MPI I/O interface was introduced,which can reduce communicational time between each node simultaneously.Introducing the parallel I/O efficiency,memory demand on single processor,acceleration ratio and relative efficiency,the efficiency of the parallel algorithm can be estimated comprehensively.The simulation result indicates that this parallel algorithm can improve the efficiency significantly,ant its relative efficiency can reach to 60%.Eventually,the earth gravity field complete to degree and order 120 and 240 are recovered on the Sugon Cluster,and the relative inversion time is only 229 s and 7 395 s respectively.In addition,the memory demand on the single node is only 205 MB and 1.57 GB,while its inversion accuracy can reach to 10-18,which indicates that the parallel algorithm in this study can be used to obtain optimal value in least square efficiently and stably.