Bulletin of the Japan Society for Industrial and Applied Mathematics
Online ISSN : 2432-1982
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Volume 29, Issue 4
Displaying 1-10 of 10 articles from this issue
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  • Memoryless Quasi-Newton Methods for Unconstrained Optimization
    Yasushi Narushima, Shummin Nakayama, Hiroshi Yabe
    2019 Volume 29 Issue 4 Pages 8-17
    Published: December 20, 2019
    Released on J-STAGE: March 31, 2020
    DOIhttps://doi.org/10.11540/bjsiam.29.4_8
    JOURNAL FREE ACCESS
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    Recently, particular attention has been paid attention to memoryless quasi-Newton methods for solving unconstrained optimization problems. Because memoryless quasi-Newton methods do not need the storage of memories for matrix and their computing cost par a iteration is low, the methods are efficient to large-scale unconstrained optimization problems. Moreover, since the methods are closely related to not only quasi-Newton methods but also nonlinear conjugate gradient methods and nonlinear three-term conjugate gradient method, it is expected that the methods are promising. This paper introduces recent studies on memoryless quasi-Newton methods.

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  • Kernel-Based Collocation Methods for Nonlinear Partial Differential Equations
    Yumiharu Nakano
    2019 Volume 29 Issue 4 Pages 18-25
    Published: December 20, 2019
    Released on J-STAGE: March 31, 2020
    DOIhttps://doi.org/10.11540/bjsiam.29.4_18
    JOURNAL FREE ACCESS
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    This paper deals with kernel-based collocation methods mainly for nonlinear parabolic partial differential equations, with a special emphasis on rigorous convergence issues. In doing so, the interpolation theory with condition-ally positive definite kernels is briefly reviewed, and a variant of Barles-Souganidis viscosity solution methods is discussed.

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