Abstract
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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This work was carried out with the financial contribution of the Human Capital and Mobility Programme of the European Union grant ERB4050PL921378.
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Arioli, M., Fassino, C. Roundoff error analysis of algorithms based on Krylov subspace methods. Bit Numer Math 36, 189–205 (1996). https://doi.org/10.1007/BF01731978
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DOI: https://doi.org/10.1007/BF01731978