Browsing by Author "Xiao, Y."

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    Expanding the applicability of an a posteriori parameter choice strategy for Tikhonov regularization of nonlinear ill-posed problems
    (Springer-Verlag Italia s.r.l., 2019) Argyros, I.K.; Cho, Y.J.; George, S.; Xiao, Y.
    We expand the applicability of an a posteriori parameter choice strategy for Tikhonov regularization of the nonlinear ill-posed problem presented in Jin and Hou (Numer Math 83:139–159, 1999) by weakening the conditions needed in Jin and Hou [13]. Using a center-type Lipschitz condition instead of a Lipschitz-type condition used in Jin and Hou [13], Scherzer et al. (SIAM J Numer Anal 30:1796–1838, 1993), we obtain a tighter convergence analysis. Numerical examples are presented to show that our results apply but earlier ones do not apply to solve equations. © 2019, The Royal Academy of Sciences, Madrid.
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    Local Convergence of Inexact Newton-Like Method under Weak Lipschitz Conditions
    (2020) Argyros, I.K.; Cho, Y.J.; George, S.; Xiao, Y.
    The paper develops the local convergence of Inexact Newton-Like Method (INLM) for approximating solutions of nonlinear equations in Banach space setting. We employ weak Lipschitz and center-weak Lipschitz conditions to perform the error analysis. The obtained results compare favorably with earlier ones such as [7, 13, 14, 18, 19]. A numerical example is also provided. 2020, Wuhan Institute Physics and Mathematics, Chinese Academy of Sciences.
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    Local Convergence of Inexact Newton-Like Method under Weak Lipschitz Conditions
    (Springer, 2020) Argyros, I.K.; Cho, Y.J.; George, S.; Xiao, Y.
    The paper develops the local convergence of Inexact Newton-Like Method (INLM) for approximating solutions of nonlinear equations in Banach space setting. We employ weak Lipschitz and center-weak Lipschitz conditions to perform the error analysis. The obtained results compare favorably with earlier ones such as [7, 13, 14, 18, 19]. A numerical example is also provided. © 2020, Wuhan Institute Physics and Mathematics, Chinese Academy of Sciences.