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Approximate quasi-Newton methods
Mathematical Programming, 1990Newton-like iterative methods for nonlinear equations on Banach spaces are considered. It is proved how the local convergence behaviour of the quasi-Newton method in the infinite dimensional setting is affected by the refinement strategy. Applications to boundary value problems and integral equations are included.
C. T. Kelley, Ekkehard W. Sachs
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Quasi-Newton Updates with Bounds
SIAM Journal on Numerical Analysis, 1987In each step of quasi-Newton methods an improved approximate solution \(x_ k\) is determined together with a new approximation \(B_ k\) of the derivative f'. Specifically, Broyden's method yields an update \(B_{k+1}\) which is the solution of the minimum problem: \(\min \{\| B-B_ k\|_ F: Bs_ k=y_ k\}.\) Here \(y_ k\) and \(s_ k\) are vectors which are ...
Calamai, Paul H., Moré, Jorge J.
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On an accelerating quasi-newton circular iteration
Applied Mathematics and Computation, 1999zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Fangyu Sun, Xiangfang Li
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A Classification of Quasi-Newton Methods
Numerical Algorithms, 2003zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Properties and numerical performance of quasi-Newton methods with modified quasi-Newton equations
Journal of Computational and Applied Mathematics, 2001 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Zhang, Jianzhong, Xu, Chengxian
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Quasi- Newton Methods for Nonlinear Equations
Journal of the ACM, 1968A unified derivation is presented of the quasi-Newton methods for solving systems of nonlinear equations. The general algorithm contains, as special cases, all of the previously proposed quasi-Newton methods.
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2008
In this chapter we take another approach toward the development of methods lying somewhere intermediate to steepest descent and Newton’s method. Again working under the assumption that evaluation and use of the Hessian matrix is impractical or costly, the idea underlying quasi-Newton methods is to use an approximation to the inverse Hessian in place of
David G. Luenberger, Yinyu Ye
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In this chapter we take another approach toward the development of methods lying somewhere intermediate to steepest descent and Newton’s method. Again working under the assumption that evaluation and use of the Hessian matrix is impractical or costly, the idea underlying quasi-Newton methods is to use an approximation to the inverse Hessian in place of
David G. Luenberger, Yinyu Ye
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2011
Nel capitolo vengono descritti i metodi Quasi-Newton (noti anche come metodi tipo-secante o metodi a metrica variabile), che costituiscono una classe di metodi per la minimizzazione non vincolata basati sulla conoscenza delle derivate prime. Il piu noto dei metodi Quasi-Newton e il metodo BFGS, del quale analizziamo, nel caso convesso, le proprieta di ...
Luigi Grippo, Marco Sciandrone
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Nel capitolo vengono descritti i metodi Quasi-Newton (noti anche come metodi tipo-secante o metodi a metrica variabile), che costituiscono una classe di metodi per la minimizzazione non vincolata basati sulla conoscenza delle derivate prime. Il piu noto dei metodi Quasi-Newton e il metodo BFGS, del quale analizziamo, nel caso convesso, le proprieta di ...
Luigi Grippo, Marco Sciandrone
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1999
Dieses Kapitel behandelt die Klasse der sogenannten Quasi—Newton—Verfahren. Diese Verfahren verwenden anstelle der exakten Hesse—Matrix der zu minimierenden Funktion eine geeignete Approximation an diese (und vermeiden damit die haufig sehr aufwendige explizite Berechnung aller zweiten partiellen Ableitungen der Zielfunktion).
Carl Geiger, Christian Kanzow
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Dieses Kapitel behandelt die Klasse der sogenannten Quasi—Newton—Verfahren. Diese Verfahren verwenden anstelle der exakten Hesse—Matrix der zu minimierenden Funktion eine geeignete Approximation an diese (und vermeiden damit die haufig sehr aufwendige explizite Berechnung aller zweiten partiellen Ableitungen der Zielfunktion).
Carl Geiger, Christian Kanzow
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A frequency domain quasi-Newton algorithm
Signal Processing, 1995zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Kostas Berberidis, Jacques Palicot
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