Hardware Architecture for Eigenvalues Computation using the Modified Jacobi Algorithm on FPGA

The calculation of eigenvalues (EVs) is important in the domain of complex computation and processing of matrices of a higher order. For real-time applications, to get superior performance, the architecture of EV computation comes in handy. In this paper, the authors have investigated an efficient architecture for EV computation using the Jacobi algorithm on the Xilinx Zed-Board FPGA evaluation platform, Artix-7 family. The iterative algorithm proves to be faster and more efficient in terms of area consumed in the FPGA architecture and also in terms of accuracy of the EV computation. The proposed architecture can take up to matrices of order $\mathbf{20}\ \mathbf{x}\ \mathbf{20}$ using the Jacobi algorithm. The algorithm also works for odd order matrices with few modifications in the input matrix. The architecture was implemented on Zynq-7000 xc7z020clg484-1 FPGA and it takes around 4216 LUTs out of 53200 LUTs for matrices of dimensions $\mathbf{4}\ \mathbf{x}\ \mathbf{4}$ .