On the convergence of Broyden’s method in Hilbert spaces

Argyros, Ioannis K.; Cho, Y. J.; Khattri, Sanjay Kumar

doi:10.1016/j.amc.2014.06.001

Cited by 2 publications

(4 citation statements)

References 11 publications

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“…. , , then lim →∞ ‖ +1 − +1 ‖ = 0, which also implies that scheme (3) and scheme (2) converge to the same fixed point of .…”

Section: Resultsmentioning

confidence: 84%

“…The main purpose of this paper is to find the conditions to guarantee lim →∞ ‖ ‖ = 0, which means that scheme (3) has a similar structure to scheme (2). Schemes (2) and (3) converge to the same fixed point of the given contraction mapping .…”

Section: Preliminariesmentioning

confidence: 99%

“…For the fixed point scheme described by (2), a question naturally arises whether we can design another iteration scheme with a similar structure to scheme (2) to approximate the fixed point. Moreover, this new scheme has a similar structure to that of the given scheme.…”

Section: Preliminariesmentioning

confidence: 99%

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An Iteration Scheme for Contraction Mappings with an Application to Synchronization of Discrete Logistic Maps

Ding

Kim

et al. 2017

Discrete Dynamics in Nature and Society

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This paper deals with designing a new iteration scheme associated with a given scheme for contraction mappings. This new scheme has a similar structure to that of the given scheme, in which those two iterative schemes converge to the same fixed point of the given contraction mapping. The positive influence of feedback parameters on the convergence rate of this new scheme is investigated. Moreover, the derived convergence and comparison results can be extended to nonexpansive mappings. As an application, the derived results are utilized to study the synchronization of logistic maps. Two illustrated examples are used to reveal the effectiveness of our results.

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“…. , , then lim →∞ ‖ +1 − +1 ‖ = 0, which also implies that scheme (3) and scheme (2) converge to the same fixed point of .…”

Section: Resultsmentioning

confidence: 84%

Section: Preliminariesmentioning

confidence: 99%

See 1 more Smart Citation

An Iteration Scheme for Contraction Mappings with an Application to Synchronization of Discrete Logistic Maps

Ding

Kim

et al. 2017

Discrete Dynamics in Nature and Society

View full text Add to dashboard Cite

show abstract

“…they showed that the iterates generated by the proposed method converge to a solution of the nonlinear complementarity problem globally. New semi-local convergence analysis was investigated by Argyros et al [6] for an inverse free Broyden's method in a Hilbert space setting. Gopalakrishna and Greiman [7] developed a method that evaluates the gradients of displacements and stresses for the structural parameters in a nonlinear finite element analysis.…”

Section: Introductionmentioning

confidence: 99%

Analysis of Second Degree of Freedom with Second Degree of Stiffness Based on Broyden’s Method

Essa¹

2017

J Civil Environ Eng

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The main purpose of this study is comparing two methods to get the convergence of two series nonlinear spring system. The key method is Broyden's method which based on the Jacobian matrix to update the inverse of the secant stiffness matrix and the results are compared with the Newton-Raphson's method. A constant force is applied to the second node in the system of two degrees of freedom (DOF). The results are compared with the first and second degree of nonlinear springs displacements differences that serially connected. The displacements at the first node are smaller than the second node and the number of iterations to reach the convergence for the second degree of difference displacements are greater than for the first degree. The main disadvantage of Broyden's method is that it becomes unstable when the number of iterations increases.

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On the convergence of Broyden’s method in Hilbert spaces

Cited by 2 publications

References 11 publications

An Iteration Scheme for Contraction Mappings with an Application to Synchronization of Discrete Logistic Maps

An Iteration Scheme for Contraction Mappings with an Application to Synchronization of Discrete Logistic Maps

Analysis of Second Degree of Freedom with Second Degree of Stiffness Based on Broyden’s Method

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