CONDITION NUMBER OF THE KRYLOV BASES AND SUBSPACES

The problems of numerical analysis with large sparse matrices often in volve a projection of this matrix onto a Krylov subspace to obtain a s maller matrix, which is used to solve the initial problem. The subspac e depends on the matrix and on an arbitrary vector. We consider a meth od to study the sensitivity of the Krylov subspace to a matrix perturb ation. This method includes a definition of the condition numbers for the computation of the Krylov basis and the Krylov subspace. A practic al method for estimating these numbers is provided. It is based on the solution of a large triangular system.