Error bounds in the isometric Arnoldi process

Error bounds for the eigenvalues computed in the isometric Arnoldi method are derived. The Arnoldi method applied to a unitary matrix U successively computes a sequence of unitary upper Hessenberg matrices H-k, k = 1, 2,... The eigenvalues of the H-k's are increasingly better approximations to eigenvalues of U. An upper bound for the distance of the spectrum of H-k from the spectrum of U, and an upper bound for the distance between each individual eigenvalue of H-k and one of U are given. Between two eigenvalues of H-k on the unit circle, there is guaranteed to lie an eigenvalue of U. The results are applied to a problem in signal processing.