Newton-like method with modification of the right-hand-side vector (Q2759094)

In order to solve a system of nonlinear equations \(F(x)=0\), where \(F: \mathbb R \to \mathbb R\) is a \(C^1\)-function, the authors propose a new method, called modification of the right-hand-size vector method (MRV). Its main idea is to modify the right-hand-size vector in the fixed Newton system NEWLINE\[NEWLINEF'(x^0)s^k_{F} = -F(x^k), NEWLINE\]NEWLINE such that the fixed Newton method thus obtained becomes more similar to the original Newton method. NEWLINENEWLINENEWLINELocal convergence of MRV is established in Section 2, while the relaxation parameter choice strategy is presented in Section 3. Section 4 presents a empirical comparison of the MRV method to other five well known methods, on a sample of nine various nonlinear systems arising in different applications. NEWLINENEWLINENEWLINEThe paper is a continuation of a previous paper by \textit{D. Herceg, N. Krejic} and \textit{Z. Luzanin} [Novi Sad J. Math. 26, No. 1, 115-127 (1996; Zbl 0948.65052)].