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New quasi-Newton method for solving systems of nonlinear equations

Ladislav Luksan(luksan***at***cs.cas.cz)
Jan Vlcek(vlcek***at***cs.cas.cz)

Abstract: In this report, we propose the new Broyden method for solving systems of nonlinear equations, which uses the first derivatives, but it is more efficient than the Newton method (measured by the computational time) for larger dense systems. The new method updates QR decompositions of nonsymmetric approximations of the Jacobian matrix, so it requires $O(n^2)$ arithmetic operations per iteration in contrast with the Newton method, which requires $O(n^3)$ operations per iteration. Computational experiments confirm the high efficiency of the new method.

Keywords: Nonlinear equations, systems of equations, trust-region methods, uasi-Newton methods, adjoint Broyden methods, numerical algorithms, numerical experiments.

Category 1: Nonlinear Optimization

Category 2: Nonlinear Optimization (Nonlinear Systems and Least-Squares )

Citation: Research Report V1233, Institute of Computer Science, Czech Academy of Sciences, Prague 2017

Download: [PDF]

Entry Submitted: 06/22/2017
Entry Accepted: 06/22/2017
Entry Last Modified: 06/22/2017

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