Abstract
We present a version of GMRES as a solver for systems of linear equations in large sparse continuation problems. Following a solution curve for a nonlinear problem with an Euler-Newton method requires the solution of linear systems. For many problems the coefficient matrices of these systems can be written as the sum of a symmetric and a rank-one unsymmetric matrix. First we show that for this specific class of systems the orthogonalization process in GMRES does not require the full effort as for general matrices and that it is possible to reduce the computational effort to about twice the effort for symmetric matrices. Secondly, a few numerical results are given for a discretization of the problem Δu + λf(u) = 0 on the square Ω = [0,1]2 and its restriction to D 4 x Z 2 -fixed-point spaces.
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© 1992 Birkhäuser Verlag Basel
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Sebastian, R. (1992). A Version of GMRES for Nearly Symmetric Linear Systems. In: Allgower, E.L., Böhmer, K., Golubitsky, M. (eds) Bifurcation and Symmetry. International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série Internationale d’Analyse Numérique, vol 104. Birkhäuser Basel. https://doi.org/10.1007/978-3-0348-7536-3_26
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DOI: https://doi.org/10.1007/978-3-0348-7536-3_26
Publisher Name: Birkhäuser Basel
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Online ISBN: 978-3-0348-7536-3
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