Roundoff error analysis of algorithms based on Krylov subspace methods

We study the roundoff error propagation in an algorithm which computes the orthonormal basis of a Krylov subspace with Householder orthonormal matrices. Moreover, we analyze special implementations of the classical GMRES algorithm, and of the Full Orthogonalization Method. These techniques approximate the solution of a large sparse linear system of equations on a sequence of Krylov subspaces of small dimension. The roundoff error analyses show upper bounds for the error affecting the computed approximated solutions.

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