PERTURBATION BOUNDS OF THE KRYLOV BASES AND ASSOCIATED HESSENBERG FORMS

This paper is devoted to further development of the method studying th e condition numbers for the computation of the Krylov orthonormal base s and subspaces K-j(A,f) = span[f, Af,..., A(j-1)f], where A is a matr ix and f is a vector. The condition numbers were obtained by means of a first-order analysis of the sensitivity of the Krylov subspaces and their orthonormal bases under small perturbations of the matrix. We gi ve perturbation bounds of the Krylov orthonormal basis and associated Hessenberg form of a matrix with respect to matrix and starting-vector perturbations. The bounds obtained depend on the condition number of the Krylov orthonormal basis. (C) 1997 Elsevier Science Inc.