On the global convergence of the block Jacobi method for the positive definite generalized eigenvalue problem

The paper proves the global convergence of a general block Jacobi method for the generalized eigenvalue problem Ax = lambda Bx with symmetric matrices A, B such that B is positive definite. The proof is made for a large class of generalized serial strategies that includes important serial and parallel strategies. The sequence of matrix pairs generated by the block method converges to (Lambda, I) , where Lambda is a diagonal matrix of the eigenvalues of the initial matrix pair (A,B) and I is the identity matrix. First, the convergence to diagonal form is proved. After that several conditions are imposed to ensure the global convergence of the block method.