Volume 7, Issue 2
Semilocal Convergence Analysis for MMN-HSS Methods under Hölder Conditions

Yang Li & Xue-Ping Guo

East Asian J. Appl. Math., 7 (2017), pp. 396-416.

Published online: 2018-02

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  • Abstract

Multi-step modified Newton-HSS (MMN-HSS) methods, which are variants of inexact Newton methods, have been shown to be competitive for solving large sparse systems of nonlinear equations with positive definite Jacobian matrices. Previously, we established these MMN-HSS methods under Lipschitz conditions, and we now present a semilocal convergence theorem assuming the nonlinear operator satisfies milder Hölder continuity conditions. Some numerical examples demonstrate our theoretical analysis.

  • Keywords

MMN-HSS method, large sparse systems of nonlinear equation, Hölder conditions, positive-definite Jacobian matrices, semilocal convergence.

  • AMS Subject Headings

65F10, 65F50, 65H10

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{EAJAM-7-396, author = {}, title = {Semilocal Convergence Analysis for MMN-HSS Methods under Hölder Conditions}, journal = {East Asian Journal on Applied Mathematics}, year = {2018}, volume = {7}, number = {2}, pages = {396--416}, abstract = {

Multi-step modified Newton-HSS (MMN-HSS) methods, which are variants of inexact Newton methods, have been shown to be competitive for solving large sparse systems of nonlinear equations with positive definite Jacobian matrices. Previously, we established these MMN-HSS methods under Lipschitz conditions, and we now present a semilocal convergence theorem assuming the nonlinear operator satisfies milder Hölder continuity conditions. Some numerical examples demonstrate our theoretical analysis.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.260416.270217a}, url = {http://global-sci.org/intro/article_detail/eajam/10756.html} }
TY - JOUR T1 - Semilocal Convergence Analysis for MMN-HSS Methods under Hölder Conditions JO - East Asian Journal on Applied Mathematics VL - 2 SP - 396 EP - 416 PY - 2018 DA - 2018/02 SN - 7 DO - http://doi.org/10.4208/eajam.260416.270217a UR - https://global-sci.org/intro/article_detail/eajam/10756.html KW - MMN-HSS method, large sparse systems of nonlinear equation, Hölder conditions, positive-definite Jacobian matrices, semilocal convergence. AB -

Multi-step modified Newton-HSS (MMN-HSS) methods, which are variants of inexact Newton methods, have been shown to be competitive for solving large sparse systems of nonlinear equations with positive definite Jacobian matrices. Previously, we established these MMN-HSS methods under Lipschitz conditions, and we now present a semilocal convergence theorem assuming the nonlinear operator satisfies milder Hölder continuity conditions. Some numerical examples demonstrate our theoretical analysis.

Yang Li & Xue-Ping Guo. (2020). Semilocal Convergence Analysis for MMN-HSS Methods under Hölder Conditions. East Asian Journal on Applied Mathematics. 7 (2). 396-416. doi:10.4208/eajam.260416.270217a
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