Monitoring the stage of diagonalization in Jacobi-type methods

Abstract

Since the stage of diagonalization of Jacobi-type methods is difficult to monitor in a parallel environment, it is usually proposed to execute a predetermined number of sweeps (iterations) on a parallel processor array. A possibility for monitoring the stage of diagonalization is essential in order to avoid the execution of a significant number of unnecessary sweeps. Based on a Lemma used for a generalized proof of the quadratic convergence of the Jacobi EVD and SVD methods a new criteria for monitoring the stage of diagonalization is derived. Using this criteria it can easily be monitored when the stage of quadratic convergence is reached (only one bit yields this information). Therefore, only the (small) number of quadratically convergent sweeps must be predetermined. A further similar criteria particularly useful for Jacobi-type methods using CORDIC-based approximate rotations is also given.<>