Convergence of scaled iterates by the Jacobi method Original Research Article

A quadratic convergence bound for scaled iterates by the serial Jacobi method for Hermitian positive definite matrices is derived. By scaled iterates we mean the matrices [diag(H(k))]−1/2H(k)[diag(H(k))]−1/2, where H(k), kgreater-or-equal, slanted0, are matrices generated by the method. The bound is obtained in the general case of multiple eigenvalues. It depends on the minimum relative separation of the eigenvalues.