An FPGA-based implementation of the MINRES algorithm

Due to continuous improvements in the resources available on FPGAs, it is becoming increasingly possible to accelerate floating point algorithms. The solution of a system of linear equations forms the basis of many problems in engineering and science, but its calculation is highly time consuming. The minimum residual algorithm (MINRES) is one method to solve this problem, and is highly effective provided the matrix exhibits certain characteristics. This paper examines an IEEE 754 single precision floating point implementation of the MINRES algorithm on an FPGA. It demonstrates that through parallelisation and heavy pipelining of all floating point components it is possible to achieve a sustained performance of up to 53 GFLOPS on the Virtex5-330T. This compares favourably to other hardware implementations of floating point matrix inversion algorithms, and corresponds to an improvement of nearly an order of magnitude compared to a software implementation.