Hierarchical block Jacobi on a cluster of multi-core Intel processors

Nowadays, it is widely accepted that exploiting all forms of parallelism is the only way to significantly improve performance. The three major forms of parallelism on a modern processor are ILP, DLP, and TLP, which are not mutually exclusive. To gain further performance improvements, MPI can be used on a cluster of computers. This paper exploits the capabilities of distributed multi-core Intel processors for accelerating the well-known singular value decomposition (SVD) based on Jacobi's algorithm. On a cluster of Fujitsu Siemens CELSIUS R550 with quad-core Intel Xeon E5410 processor running at 2.33 GHz, hierarchical block Jacobi is implemented and evaluated. On eight nodes, our results show a performance of 184.56 double-precision GFLOPS by exploiting multi-threading, SIMD, and memory hierarchy techniques. Moreover, on large matrix size, the speedups of the hierarchical block Jacobi algorithm over sequential one-sided Jacobi improve from 17.33 using superscalar implementation to 30.46, 62.94, and 86.55, by exploiting the SIMD, multi-threading, and multi-threading SIMD techniques, respectively.