A modified generalized Newton method applied to solving absolute value equations

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Abstract

In this paper, we present a modified generalized Newton method (MGNM) for solving absolute value equation (AVEs) Ax −|x| =b. Some known iterative schemes are special cases of our method. We prove that the generated sequence of iterates is well defined and converges linearly under condition $\left\|A^{-1}\right\|<\frac{1}{3\left(2 t_{0}+t_{1}\right)+1}$ (t₀ and t₁ are constants greater than or equal to 0, and not both zero). Compared to Newton’s method, the MGNM can guarantee the convergence of the iterative method under weaker conditions. Numerical experiments on various types of problems are conducted to illustrate the superior efficiency and accuracy of the proposed method, showing its superiority over some existing methods.

Keywords

absolute value equations / modified generalized Newton method / convergence

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