Perturbation bounds of the krylov bases and associated hessenberg forms

This paper is devoted to further development of the method studying the condition numbers for the computation of the Krylov orthonormal bases and sub-spaces 1-1, where A is a matrix and ƒ 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 give 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