“Quasi-Newton inverse least squares method”的意思、由来-开放百科全书

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Quasi-Newton inverse least squares method

释义

References

In numerical analysis, the quasi-Newton inverse least squares method is a quasi-Newton method for finding roots of functions of several variables. It was originally described by Degroote et al. in 2009.^[1]

Newton's method for solving {{math|f(x) {{=}} 0}} uses the Jacobian matrix, {{math|J}}, at every iteration. However, computing this Jacobian is a difficult (sometimes even impossible) and expensive operation. The idea behind the quasi-Newton inverse least squares method is to build up an approximate Jacobian based on known input–output pairs of the function {{math|f}}.

Haelterman et al. also showed that when the quasi-Newton inverse least squares method is applied to a linear system of size {{math|n × n}}, it converges in at most {{math|n + 1}} steps, although like all quasi-Newton methods, it may not converge for nonlinear systems.^[2]

The method is closely related to the quasi-Newton least squares method.

References

1. ^{{cite journal |author1=J. Degroote |author2=R. Haelterman |author3=S. Annerel |author4=A. Swillens |author5=P. Segers |author6=J. Vierendeels | title= An interface quasi-Newton algorithm for partitioned simulation of fluid-structure interaction| journal=Proceedings of the International Workshop on Fluid–Structure Interaction. Theory, Numerics and Applications. S. Hartmann, A. Meister, M. Schfer, S. Turek (Eds.), Kassel University Press, Germany | year=2008}}
2. ^{{cite journal | doi=10.1016/j.cam.2013.08.020|author1=R. Haelterman |author2=J. Petit |author3=B. Lauwens |author4=H. Bruyninckx |author5=J. Vierendeels | title= On the Non-Singularity of the Quasi-Newton-Least Squares Method| journal=Journal of Computational and Applied Mathematics| volume=257 | year=2014 | pages=129–131}}

2 : Optimization algorithms and methods|Least squares

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