Roundoff error analysis of algorithms based on Krylov subspace methods |
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Authors: | M Arioli C Fassino |
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Institution: | (1) Istituto di Analisi Numerica, Consiglio Nazionale delle Ricerche, via Abbiategrasso 209, 1-27100 Pavia, Italy;(2) II Universita degli Studi di Roma, Dipartimento di Matematica, via Ricerca Scientifica 5, 00133 Roma, Italy |
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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.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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Keywords: | Krylov subspace methods GMRES roundoff error analysis |
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