Quasi-Newton least squares method
In numerical analysis, the quasi-Newton least squares method is a quasi-Newton method for finding roots in variables. It was originally described by Rob Haelterman et al. in 2009.
Newton's method for solving uses the Jacobian matrix,, at every iteration. However, computing this Jacobian is a difficult and expensive operation. The idea behind the quasi-Newton least squares method is to build up an approximate Jacobian based on known input–output pairs of the function.
Haelterman et al. also showed that when the quasi-Newton least squares method is applied to a linear system of size, it converges in at most steps, although like all quasi-Newton methods, it may not converge for nonlinear systems.
The method is closely related to the quasi-Newton inverse least squares method.
