Implementation in Fpgas of Jacobi Method to Solve the Eigenvalue and Eigenvector Problem

Abstract

This work shows a modular architecture based on FPGA's to solve the eigenvalue problem according to the Jacobi method. This method is able to solve the eigenvalues and eigenvectors concurrently. The main contribution of this work is the low execution time compared with other sequential algorithms, and minimal internal FPGA consumed resources, mainly due to the fact of using the CORDIC algorithm. Two CORDIC modules have been designed to solve the trigonometric operations involved. A parallel CORDIC architecture is proposed as it is the best option to compute the eigenvalues with this method. Both CORDIC modules can work in rotation and vector mode. The whole system has been done in VHDL language, attempting to optimize the design.