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 high��order dense symmetrical positive define matrix with Gauss��Jordan 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.
