Parallelizable eigenvalue decomposition techniques via the matrix sector function

Many modern high-resolution spectral estimators in signal processing and control make use of the subspace information afforded by the singular value decomposition of the data matrix, or the eigenvalue decomposition of the covariance matrix. The derivation of these estimators involves some form of matrix decomposition. In this paper, new computational techniques for obtaining eigenvalues and eigenvectors of a square matrix are presented. These techniques are based on the matrix sector function which can be applied to break down a given matrix into matrices of smaller dimensions and consequently this approach is suitable for parallel implementation. Finally, an example which illustrates the proposed method is provided