Computing the least squares inverse of sparse matrices on a network of clusters

This paper describes the calculation of the least square inverse of sparse matrices and the use of load balancing schemes for parallel processing in a heterogeneous environment. Due to the variation of number of non zero entries to be calculated row wise, as well as the difference of processor speeds, load imbalance may occur and have an impact on the performance. To improve the performance by keeping processors as busy as possible the redistribution of tasks and data is needed. We present an architecture and implementation outlines of a few load balancing schemes featured with one-sided communications in a framework of multithreading. We show through our tests that the use of load balancing schemes can improve the performance in some cases.