Parallel direct solution of linear equations on FPGA-based machines

The efficient solution of large systems of linear equations represented by sparse matrices appears in many tasks. LU factorization followed by backward and forward substitutions is widely used for this purpose. Parallel implementations of this computation-intensive process are limited primarily to supercomputers. New generations of field-programmable gate array (FPGA) technologies enable the implementation of system-on-a-programmable-chip (SOPC) computing platforms that provide many opportunities for configurable computing. We present the design and implementation of a parallel machine for LU factorization on an SOPC board, using multiple instances of a soft processor. A highly parallel block-diagonal-bordered (BDB) algorithm for LU factorization is mapped to our multiprocessor. Our results prove the viability of our FPGA-based approach.