Convergence Domains for Some Iterative Processes in Banach Spaces Using Outer or Generalized Inverses |
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Authors: | Ioannis K. Argyros |
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Affiliation: | (1) Department of Mathematics, Cameron University, Lawton, Oklahoma, 73505 |
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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 such that starting from any point of 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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Keywords: | Inexact Newton-like methods Banach space outer inverse inner inverse generalized inverse |
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