A classification of quasi-Newton methods. (English) Zbl 1030.65053

Brezinski, C.

Numer. Algorithms 33, No. 1-4, 123-135 (2003).

Summary: We consider quasi-Newton methods of the form \(x_{k+1}=x_k+\Lambda_kf(x_k), k=0,1,\dots \), for the solution of the system of nonlinear equations \(f(x)=0\). We present a classification of such methods based on different structures for the matrix \(\Lambda_k\) and various criteria for its computation, issued from three different formulae. Many known methods can be put into this framework and new methods are also obtained.

MSC:

65H10

Numerical computation of solutions to systems of equations

Keywords:

nonlinear equations; quasi-Newton methods; comparison of methods