Institute of Electrical & Electronic Engineers
Acceleration of ubiquitous linear algebra operations such as solving systems of linear equations or determining the eigen-values of a matrix has the potential to enable new applications in all areas of engineering and science. The authors consider the problem of enabling fixed-point implementations of linear algebra kernels to match the strengths of the Field-Programmable Gate Array (FPGA). Algorithms for solving linear equations, finding eigen-values or finding singular values are typically nonlinear and recursive making the problem of establishing analytical bounds on variable dynamic range non-trivial. Current approaches fail to provide tight bounds for this type of algorithms.