A modified generalized Newton method applied to solving absolute value equations
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 $ \|A^{-1}\| < \frac{1}{3(2t_0+t_1)+1} $ ($ t_0 $ and $ t_1 $ 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.
Fields of Study & Subjects
Iterative Methods for Nonlinear Equations
Heat Transfer and Numerical Methods
Matrix Theory and Algorithms
Publication details
- Journal / source
- Electronic Research Archive
- Publisher
- American Institute of Mathematical Sciences (AIMS)
- Volume
- 34
- Issue
- 8
- Pages
- 5352–5366
- Publication date
- 1 January 2026