Perturbation bounds of the Krylov bases and associated Hessenberg forms (Q1369342)

The author proves a perturbation formula for orthonormal bases of the Krylov subspace span \([f_1,A_1f_1,\ldots,A_1^{j-1}f_1]\) for a matrix \(A_1\) and a vector \(f_1\), in terms of the condition number of an orthonormal basis for the unperturbed matrix and vector \(A,f\) and the \(L^2\) norms of \(A_1-A\), \(f_1-f\).