Abstract
A solid understanding of convergence behaviour is essential to the design and analysis of iterative methods. In this chapter we explore the convergence of inexact iterative methods in general, and inexact Newton methods in particular. A direct relationship between the convergence of inexact Newton methods and the forcing terms is presented, and the practical implications concerning computational effort are discussed and illustrated through numerical experiments.
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References
Dembo, R.S., Eisenstat, S.C., Steihaug, T.: Inexact Newton methods. SIAM J. Numer. Anal. 19(2), 400–408 (1982)
Ortega, J.M., Rheinboldt, W.C.: Iterative Solution of Nonlinear Equations in Several Variables. Academic Press, New York (1970)
Dennis Jr, J.E., Schnabel, R.B.: Numerical Methods for Unconstrained Optimization and Nonlinear Equations. Prentice Hall, New Jersey (1983)
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Idema, R., Lahaye, D.J.P. (2014). Convergence Theory. In: Computational Methods in Power System Analysis. Atlantis Studies in Scientific Computing in Electromagnetics, vol 1. Atlantis Press, Paris. https://doi.org/10.2991/978-94-6239-064-5_5
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DOI: https://doi.org/10.2991/978-94-6239-064-5_5
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