High-Performance Architecture for the Conjugate Gradient Solver on FPGAs

The conjugate gradient (CG) solver is an important algorithm for solving the symmetric positive define systems. However, existing CG architectures on field-programmable gate arrays (FPGAs) either need aggressive zero padding or can only be applied for small matrices and particular matrix sparsity patterns. This brief proposes a high-performance architecture for the CG solver on FPGAs, which can handle sparse linear systems with arbitrary size and sparsity pattern. Furthermore, it does not need aggressive zero padding. Our CG architecture mainly consists of a high-throughput sparse matrix-vector multiplication design including a multi-output adder tree, a reduction circuit, and a sum sequencer. Our experimental results demonstrate that our CG architecture can achieve speedup of 4.62X-9.24X on a Virtex5-330 FPGA, relative to a software implementation.