Sub Tasks Matrix Multiplication Algorithm (STMMA)

Several parallel matrix multiplications developed since four decades based on decomposing the multiplied matrices into smaller size blocks, the blocks will be distributed among the processors to run matrix multiplication in shorter time than when only one processor will run the whole matrix multiplications. All parallel matrix multiplications algorithms suffer from three points: C The optimal size of the block of the decomposed matrices. C The optimal number and size of the exchanged messages between the processors. C Data dependency between the processors. And some algorithms suffer from fourth point, which is load balance especially with non-square matrix multiplications. In this paper we will introduce new parallel matrix multiplications to overcome the above four drawbacks, which will result in vast difference in performance in terms of time and load balance. For example, for a matrices multiplication of 5000×5000, it consumes 2812 seconds using cannon algorithm, while only 712 seconds needed using STMMA to accomplish the same task using MPI library, which implies 4 times faster. We have used Processors Intel(R) Core(TM) i5 CPU 760 @2.80GHz 2.79 GHz, Installed memory (RAM) 4.00 GB, System type: 64-bit Operating System, Windows 7 Professional. We have coded the algorithms using Microsoft C++ ver. 6, with MPI Library.