Some Convergence Properties of Broyden's Method

Gay, David

doi:10.3386/w0175

Cited by 13 publications

(15 citation statements)

References 3 publications

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“…On the other hand, Gay showed in 1979 [5] He has also proved that Broyden's good method enjoys local 2m-step Q-quadratlc convergence on non-llnear systems.…”

Section: Introductionmentioning

confidence: 99%

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On a general convergence for Broyden like update method

Sen

Chattopaohyay

Saha

1990

International Journal of Mathematics and Mathematical Sciences

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“…On the other hand, Gay showed in 1979 [5] He has also proved that Broyden's good method enjoys local 2m-step Q-quadratlc convergence on non-llnear systems.…”

Section: Introductionmentioning

confidence: 99%

“…[5]. Broyden [7] showed that both Broyden's good and bad methods converge locally at least Q-superlInearly.…”

Section: Introductionmentioning

confidence: 99%

On a general convergence for Broyden like update method

Sen

Chattopaohyay

Saha

1990

International Journal of Mathematics and Mathematical Sciences

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“…One of the results showed that Broyden's update method gives a reduction of the number of iterations relative to the Newton method and it gives a higher rate of convergence. The convergence of the Broyden method has been extensively studied in [14] and [15].…”

Section: Introductionmentioning

confidence: 99%

Determination of Gas Pressure Distribution in a Pipeline Network using the Broyden Method

Sidarto

Kania

Mucharam

et al. 2017

J. Eng. Technol. Sci.

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Abstract.A potential problem in natural gas pipeline networks is bottlenecks occurring in the flow system due to unexpected high pressure at the pipeline network junctions resulting in inaccurate quantity and quality (pressure) at the end user outlets. The gas operator should be able to measure the pressure distribution in its network so the consumers can expect adequate gas quality and quantity obtained at their outlets. In this paper, a new approach to determine the gas pressure distribution in a pipeline network is proposed. A practical and userfriendly software application was developed. The network was modeled as a collection of node pressures and edge flows. The steady state gas flow equations Panhandle A, Panhandle B and Weymouth to represent flow in pipes of different sizes and a valve and regulator equation were considered. The obtained system consists of a set of nonlinear equations of node pressures and edge flowrates. Application in a network in the field involving a large number of outlets will result in a large system of nonlinear equations to be solved. In this study, the Broyden method was used for solving the system of equations. It showed satisfactory performance when implemented with field data.

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“…Hence, no 'extra' information needs to be computed in order to update B k to yield B k+1 . The most successful quasi-Newton update for the nonlinear equations problem, often referred to as the secant update [2,10], is the matrix solution to the convex optimization problem,…”

Section: Introductionmentioning

confidence: 99%

A secant method for nonlinear least-squares minimization

Coleman

Liu

2010

Comput Optim Appl

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Quasi-Newton methods have played a prominent role, over many years, in the design of effective practical methods for the numerical solution of nonlinear minimization problems and in multi-dimensional zero-finding. There is a wide literature outlining the properties of these methods and illustrating their performance [e.g., [8]]. In addition, most modern optimization libraries house a quasi-Newton collection of codes and they are widely used. The quasi-Newton contribution to practical nonlinear optimization is unchallenged.In this paper we propose and investigate an efficient quasi-Newton (secant) approach to the nonlinear least-squares problem, made practical due to the selective application of automatic differentiation (AD) technology. We also observe that AD technology can increase the efficiency of the standard quasi-Newton (positive definite secant) approach to the full nonlinear minimization approach to this problem and we compare these two AD-assisted methods. Finally, we compare the AD-assisted approaches to a standard globalized Gauss-Newton method.

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Some Convergence Properties of Broyden's Method

Cited by 13 publications

References 3 publications

On a general convergence for Broyden like update method

On a general convergence for Broyden like update method

Determination of Gas Pressure Distribution in a Pipeline Network using the Broyden Method

A secant method for nonlinear least-squares minimization

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