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