Rapid Prototyping Projection Algorithms with FPGA Technology

Linear systems with Toeplitz coefficient matrices often appear in applied science problems. Systems of this form arise as a result of finite difference methods when applied to approximate differential equations with boundary conditions. The sparse structure of Toeplitz matrices lend themselves well to iterative algorithms, such as projection methods, and are favored techniques for solving large systems. Field programmable gate arrays (FPGAs) have been growing in popularity among the scientific community due to the potential for increased performance when evaluating mathematical operations. The regular, sparse, structure inherent in Toeplitz systems makes it suitable for FPGA acceleration. Here, a framework is developed to support the efficient development of projection algorithms in an FPGA. Results of applying the framework to two projection algorithms are presented.