Improving load balance of parallel factorization of block iterative methods

The methods for the solution of systems of linear equations can be analysed under two main headings: direct and iterative methods. Hybrid methods, which combine direct and iterative methods, represent a new alternative. Block Cimmino is a hybrid method used in the solution of systems of linear equations and is very suitable for parallel use. Since the convergence rate of the block Cimmino method depends on the orthogonality between the row blocks, the method of obtaining the row blocks becomes important. When obtaining row blocks, it is important that the row blocks are balanced and orthogonal to ensure parallel load balancing. Partitioning methods are used to ensure this. The aim of this study is to obtain better row blocks by making improvements to GRIP, one of the pioneering partitioning methods. Results obtained on supercomputers have shown that it provides up to 10 times faster parallel factorization and up to 7 times less memory consumption.