Some Convergence Properties of Broyden’s Method

Gay, David M.

doi:10.1137/0716047

Cited by 83 publications

(29 citation statements)

References 9 publications

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“…Ideally, one would like to choose t k such that \\e k+1 ( 2) is t k =1. Somewhat surprisingly, this choice guarantees that the resulting method -at least in theory -terminates after at most 2n steps with the exact solution of (1.1), as was shown by GAY [9] (cf. also [10]).…”

Section: Line Search Principlesmentioning

confidence: 69%

Fast secant methods for the iterative solution of large nonsymmetric linear systems

Deuflhard

Freund

Walter

1990

IMPACT of Computing in Science and Engineering

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Section: Line Search Principlesmentioning

confidence: 69%

Fast secant methods for the iterative solution of large nonsymmetric linear systems

Deuflhard

Freund

Walter

1990

IMPACT of Computing in Science and Engineering

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“…In order to estimate the pseudo-Hessian B, different iterative algorithms have been used and published over many years: the Davidon 56 method, the methods described by Fletcher 57,58 in his book, the Broyden method, 59,60 (symmetric rank 1 54 ) and the class of Broyden methods. 54,59 All these methods use the Sherman-Morrison formula 54 to invert the pseudo-Hessian matrix B.…”

Section: Non-linear Multi-variate Optimization Methodsmentioning

confidence: 99%

Evaluating the effect of a driver’s behaviour on the range of a battery electric vehicle

Álvarez

López

Torre

2014

Proceedings of the Institution of Mechanical Engineers, Part D:

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A battery electric vehicle uses the electric energy stored in a battery to supply power to the electric motor. The estimation of an accurate electric range is an important matter because of the consumer's fear of running out of electricity while driving, often referred to as 'range anxiety'. This article both analyses and quantifies the influence of driving aggressiveness on the battery life. In order to achieve this, a modification of the New European Driving Cycle is performed, simulating progressively more aggressive behaviours. The calculation of the energy consumption and, accordingly, of the vehicle range is performed through a complete vehicle model implemented in MATLAB/Simulink, where an improvement in the battery model is presented, allowing faster processing. The methodology presented can contribute to more efficient management of the power consumed by the vehicle and a decrease in range anxiety.

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“…For linear problems, the method is known to show superlinear convergence [31] and it needs at most 2mn iteration to reach the solution (Gay's theorem [21]). 2.…”

Section: Broyden's Good Methodsmentioning

confidence: 99%

Accelerating Existing Non-Blind Image Deblurring Techniques through a Strap-On Limited-Memory Switched Broyden Method

Lahouli

Haelterman

Degroote

et al. 2018

IEICE Trans. Inf. & Syst.

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SUMMARYVideo surveillance from airborne platforms can suffer from many sources of blur, like vibration, low-end optics, uneven lighting conditions, etc. Many different algorithms have been developed in the past that aim to recover the deblurred image but often incur substantial CPU-time, which is not always available on-board. This paper shows how a "strap-on" quasi-Newton method can accelerate the convergence of existing iterative methods with little extra overhead while keeping the performance of the original algorithm, thus paving the way for (near) real-time applications using on-board processing. key words: image deblurring, quasi-Newton, limited-memory, switched Broyden method

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Some Convergence Properties of Broyden’s Method

Cited by 83 publications

References 9 publications

Fast secant methods for the iterative solution of large nonsymmetric linear systems

Fast secant methods for the iterative solution of large nonsymmetric linear systems

Evaluating the effect of a driver’s behaviour on the range of a battery electric vehicle

Accelerating Existing Non-Blind Image Deblurring Techniques through a Strap-On Limited-Memory Switched Broyden Method

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