CJS: Custom Jacobi Solver

The classic Jacobi method, widely used for solving linear systems, is slow, especially when dealing with large matrices. This paper proposes a Custom Jacobi Solver (CJS) for large-scale linear systems. It is based on a column-wise Jacobi step operation which allows for increased dependence distance, enabling deep pipelining. Our solver allows customisation at run time between the classic Jacobi method and its more convergence efficient-counterpart, the weighted Jacobi method. It can be dynamically scaled to multiple FPGAs by appropriately partitioning the matrix data among the FPGAs. After evaluating our solver on a number of different datasets, CJS proves to be up to 71 times faster when comparing an 8-FPGA solution with a 12-core CPU C++ implementation.