Diederik R. Fokkema, Gerard L. G. Sleijpen, Henk A. Van der Vorst  Home/Search
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Abstract: Classical iteration methods for linear systems, such as Jacobi Iteration, can be accelerated considerably by Krylov subspace methods like GMRES. In this paper, we describe how Inexact Newton methods for nonlinear problems can be accelerated in a similar way and how this leads to a general framework that includes many well-known techniques for solving linear and nonlinear systems, as well as new ones. Inexact Newton methods are frequently used in practice to avoid the expensive exact solution of ... (Update)
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...update the approximate solution and GMRES in the inner loop to compute a new search direction from a correction equation. As argued in [7], Jacobi Davidson with (2) can be viewed as the eigenvalue version of GMRESR, while Jacobi Davidson with (3) is the analogue of GCRO. GCRO...
.... Krylov basis with sophisticated injecting technique [20] and application of Krylov like projections directly on the nonlinear level [22, 6, 8], are only some possibilities. These techniques are mainly aimed to capture the information, delivered by Krylov methods during...
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BibTeX entry: (Update)
D.R. Fokkema, G.L.G. Sleijpen, and H.A. van der Vorst, Accelerated Inexact Newton Schemes for Large Systems of Nonlinear Equations, SIAM J. Scient. Comput., 19 (2), pp.657-674, 1998. http://citeseer.ist.psu.edu/article/fokkema95accelerated.html More
@article{ fokkema98accelerated,
author = "Diederik R. Fokkema and Gerard L. G. Sleijpen and Henk A. Van der Vorst",
title = "Accelerated Inexact {Newton} Schemes for Large Systems of Nonlinear Equations",
journal = "SIAM Journal on Scientific Computing",
volume = "19",
number = "2",
pages = "657--674",
year = "1998",
url = "citeseer.ist.psu.edu/article/fokkema95accelerated.html" }
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