Fully explicit and super-efficient iterative methods for solving systems of nonlinear equations - Zhanlav, Tugal; Otgondorj, Khuder (Mongolian Mathematical Journal, 2025)
In this paper, we propose novel fully explicit and super-efficient iterative methods for solving systems of nonlinear equations. The proposed methods are matrix-free and do not require expensive operations such as matrix inversion or matrix multiplication; instead, they involve only vector operations. As a result, they are easy to implement with O(n2) computational complexity, whereas other existing iterative methods typically have O(n3) complexity. Numerical experiments are presented to demonstrate the effectiveness, robustness, and superior performance of the proposed iterative methods.