Optimal Convergence of the Simultaneous Iteration Method for Normal Matrices

Simultaneous iteration methods are extensions of the power method that were devised for approximating several dominant eigenvalues of a matrix and the corresponding eigenvectors. The convergence analysis of these methods has been given for both hermitian and nonhermitian matrices. In this paper we concentrate on normal matrices which include also the hermitian matrices, and provide a rigorous analysis for a common version of simultaneous iteration methods. We improve on some of the known results and derive some new ones as well. We also present a detailed analysis concerning the formation of spurious eigenvalue approximations. T ec hn io n C om pu te r Sc ie nc e D ep ar tm en t T eh ni ca l R ep or t C S0 72 5. re vi se d 19 92