Matrix Operations on a Multicomputer System with Switchable Main Memory Modules and Dynamic Control

This paper presents an analysis and evaluation of the performance of a multicomputer system (SM3) in supporting two basic matrix operations, namely multiplication and inversion. The system supports the efficient execution of the above mentioned operations by 1) achieving a high-bandwidth data transfer among computers by switching main memory modules, 2) supporting network partitioning, 3) employing a hardware communication and synchronization scheme, 4) using a distributed control technique, and 5) providing means to dynamically transfer control. Timing equations are derived and evaluated in an attempt to analyze the performance. Different cases which arise due to the relative sizes of memory modules and matrices during matrix multiplication are analyzed. The cases of partial and maximal pivoting during inversion are also analyzed. The SM3 system is compared quantitatively and qualitatively to a hypercube architecture.