A rigorous inexact Newton method with applications to boundary value problems
DOI:
https://doi.org/10.5540/03.2021.008.01.0345Keywords:
Differential equations, Inexact Newton Method, Newton-Kantorovich Theorem, Rigorous NumericsAbstract
We introduce a semi-local theorem for the feasibility and convergence of the inexact Newton method Uk+i = Uk — DF(uk)~rF(uk) + rfc, where rk represents the error in each step. Unlike the previous results of this type in the literature, we prove the feasibility of the inexact Newton method under the minor hypothesis that the error rk is bounded by a small constant to be computed, and moreover we prove results concerning the convergence of the sequence Uk to the solution under this hypothesis. We present an application of the method to rigorously compute zeros for two-point boundary value problems.
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References
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