A sorted Jacobi algorithm and its parallel implementation

For the eigenvalue decomposition in angle symmetric matrices, a new sorted Jacobi algorithm (S-Jacobi) is proposed. This algorithm sorts the eigenvalues automatically by exploiting both inner and outer angles in each Jacobi rotation. With the condition of convergence that can be easily satisfied in practice, the convergence speed of S-Jacobi is faster than conventional Jacobi algorithms that do not involve eigenvalue sorting. Furthermore, the rotation angle computing circuit proposed for the parallel implementation of S-Jacobi needs only small additional hardware with respect to the case of conventional Jacobi algorithms.