Abstract
We provide a semilocal Ptak–Kantorovich-type analysis for inexact Newton-like methods using outer and generalized inverses to approximate a locally unique solution of an equation in a Banach space containing a nondifferentiable term. We use Banach-type lemmas and perturbation bounds for outer as well as generalized inverses to achieve our goal. In particular we determine a domain Ω such that starting from any point of Ω our method converges to a solution of the equation. Our results can be used to solve undetermined systems, nonlinear least-squares problems, and ill-posed nonlinear operator equations in Banach spaces. Finally, we provide two examples to show that our results compare favorably with earlier ones.
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Argyros, I.K. Convergence Domains for Some Iterative Processes in Banach Spaces Using Outer or Generalized Inverses. Journal of Computational Analysis and Applications 1, 87–104 (1999). https://doi.org/10.1023/A:1022670604314
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DOI: https://doi.org/10.1023/A:1022670604314