Quasi-Newton Inverse Least Squares Method
In numerical analysis, The Quasi-Newton Inverse Least Squares Method is a quasi-Newton method for finding roots in n variables. It was originally described by Degroote et al. in 2009.[1]
Newton's method for solving f(x) = 0 uses the Jacobian matrix, 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 f.
Haelterman et al. also showed that when the Quasi-Newton Inverse Least Squares Method is applied to a linear system of size n × n, it converges in at most 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
- ↑ J. Degroote; R. Haelterman; S. Annerel; A. Swillens; P. Segers; J. Vierendeels (2008). "An interface quasi-Newton algorithm for partitioned simulation of fluid-structure interaction". 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.
- ↑ R. Haelterman; J. Petit; B. Lauwens; H. Bruyninckx; J. Vierendeels (2014). "On the Non-Singularity of the Quasi-Newton-Least Squares Method". Journal of Computational and Applied Mathematics. 257: 129–131. doi:10.1016/j.cam.2013.08.020.