Double-precision Gauss-Jordan Algorithm with Partial Pivoting on FPGAs

This work presents an architecture to compute matrix inversions in a reconfigurable digital system, benefiting from embedded processing elements present in FPGAs, and using double precision floating point representation. The main module of this system is the processing component for the Gauss-Jordan elimination. This component consists of other smaller arithmetic units, organized in pipeline. These units maintain the accuracy in the results without the need to internally normalize and de-normalize the floating-point data. The implementation of the operations takes advantage of the embedded processing elements available in the Virtex-5 FPGA. This implementation shows performance and resource consumption improvements when compared with "traditional" cascaded implementations of the floating point operators. Benchmarks are done with solutions implemented previously in FPGA and software, such as Matlab and Scilab.