Simultaneous iteration for the matrix eigenvalue problem

Let B be a given positive definite Hermitian matrix, and assume the matrix P satisfies the “normality” condition PB^?1P^HB=B^?1P^HBP, where P^H denotes the Hermitian of P. In this paper, we develop an accelerated version of simultaneous iteration for partial solution of the eigenproblem Px=λx. Convergence together with sharp error bounds is obtained. The results are then applied to the solution of the symmetric eigenproblem Ax=λBx, where the algorithms are shown to be improvements over existing techniques.