Subspace projection variants on Newton's method
The paper deals with a variant of Newton's method for solving a not necessarily square system \(F(x) = 0\) of nonlinear equations. The basic iteration step \(x_{n+1} = x_ n + Y_ ny_ n\) requires a solution of the square linear system \(J_ ny_ n = - F(x_ n)\) with \(J_ n = F'(x_ n) Y_ n\), where \(F'(x_ n)\) denotes the Jacobian and \(Y_ n\) is an appropriate right preconditioner of the Jacobian. This class includes the so-called angle method by \textit{D. D. Georg} and \textit{R. F. Keller} [Comput. Math. Appl. 2, 225-232 (1976; Zbl 0375.65027)] as well as the classical Newton method. The method can be seen as a projection method on a (possibly lower-dimensional) subspace. The convergence of the method for affine problems and the local convergence for nonlinear problems are analyzed and numerical examples are given.
scientific article; zbMATH DE number 579946
scientific article