Bit-level systolic algorithm for the symmetric eigenvalue problem

Abstract

An arithmetic algorithm is presented which speeds up the parallel Jacobi method for the eigen-decomposition of real symmetric matrices. After analyzing the elementary mathematical operations in the Jacobi method (i.e. the evaluation and application of Jacobi rotations), the author devises arithmetic algorithms that effect these mathematical operations with few primitive operations (i.e. few shifts and adds) and enable the most efficient use of the parallel hardware. The matrices to which the plane Jacobi rotations are applied are decomposed into even and odd parts, enabling the application of the rotations from a single side and thus removing some sequentiality from the original method. The rotations are evaluated and applied in a fully concurrent fashion with the help of an implicit CORDIC algorithm. In addition, the CORDIC algorithm can perform rotations with variable resolution, which lead to a significant reduction in the total computation time.<>