Quasi-Newton's method with correction.
Herceg, Dragoslav, Krejić, Nataša, Lužanin, Zorana (1996)
Novi Sad Journal of Mathematics
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Herceg, Dragoslav, Krejić, Nataša, Lužanin, Zorana (1996)
Novi Sad Journal of Mathematics
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G. Schuller (1974/75)
Numerische Mathematik
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Mahsa Nosrati, Keyvan Amini (2024)
Applications of Mathematics
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We present a new diagonal quasi-Newton method for solving unconstrained optimization problems based on the weak secant equation. To control the diagonal elements, the new method uses new criteria to generate the Hessian approximation. We establish the global convergence of the proposed method with the Armijo line search. Numerical results on a collection of standard test problems demonstrate the superiority of the proposed method over several existing diagonal methods.
Pierpaolo Omari, Igor Moret (1991)
Numerische Mathematik
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J.E. jr. DENNIS (1968)
Numerische Mathematik
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T.J. Ypma (1984)
Numerische Mathematik
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Joseph W. Jerome (1987)
Numerische Mathematik
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Polyak, B.T. (2004)
Journal of Mathematical Sciences (New York)
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Argyros, Ioannis K. (1998)
Southwest Journal of Pure and Applied Mathematics [electronic only]
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Ioannis K. Argyros, Santhosh George (2015)
Applicationes Mathematicae
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We present a local convergence analysis of inexact Newton-like methods for solving nonlinear equations. Using more precise majorant conditions than in earlier studies, we provide: a larger radius of convergence; tighter error estimates on the distances involved; and a clearer relationship between the majorant function and the associated least squares problem. Moreover, these advantages are obtained under the same computational cost.
Ioannis K. Argyros, Santhosh George (2019)
Commentationes Mathematicae Universitatis Carolinae
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A. Cordero et. al (2010) considered a modified Newton-Jarratt's composition to solve nonlinear equations. In this study, using decomposition technique under weaker assumptions we extend the applicability of this method. Numerical examples where earlier results cannot apply to solve equations but our results can apply are also given in this study.
Ioannis K. Argyros (2006)
Applicationes Mathematicae
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The Newton-Mysovskikh theorem provides sufficient conditions for the semilocal convergence of Newton's method to a locally unique solution of an equation in a Banach space setting. It turns out that under weaker hypotheses and a more precise error analysis than before, weaker sufficient conditions can be obtained for the local as well as semilocal convergence of Newton's method. Error bounds on the distances involved as well as a larger radius of convergence are obtained. Some numerical...
Ioannis K. Argyros (2002)
Applicationes Mathematicae
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We present a local and a semilocal analysis for Newton-like methods in a Banach space. Our hypotheses on the operators involved are very general. It turns out that by choosing special cases for the "majorizing" functions we obtain all previous results in the literature, but not vice versa. Since our results give a deeper insight into the structure of the functions involved, we can obtain semilocal convergence under weaker conditions and in the case of local convergence a larger convergence...
C.T. Kelley, E.W. Sachs (1987)
Numerische Mathematik
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