An algorithm and architecture based on orthonormal μ-rotations for computing the symmetric EVD

In this paper an algorithm and architecture for computing the eigenvalue decomposition (EVD) of a symmetric matrix is presented. The EVD is computed using a Jacobi-type method, where the angle of the rotations is approximated by an angle k , corresponding to an orthonormal {rotation. These orthonormal {rotations are based on the idea of CORDIC and share the property that performing the rotation requires a minimal number of shift{add operations. We present various methods of construction for such orthonormal {rotations of increasing complexity. Moreover, the computations to determine which angle k to use in the approximation of the optimal angle, can itself be expressed purely in orthonormal {rotations on the matrix data. The complexity of the used type of orthonormal {rotation decreases during the diagonalization of the matrix. A signiicant reduction of the number of required shift{add operations is achieved. All types of fast, orthonormal {rotations (and the computation to determine the optimal angle) can be implemented as a cascade of only four basic types of shift{add stages. These stages can be executed on a modiied sequential oating-point CORDIC architecture, making the presented algorithm highly suited for VLSI{implementation.