@Article{cmes.2022.021655,
AUTHOR = {Chein-Shan Liu, Essam R. El-Zahar, Yung-Wei Chen},
TITLE = {Nonlinear Algebraic Equations Solved by an Optimal Splitting-Linearizing Iterative Method},
JOURNAL = {Computer Modeling in Engineering \& Sciences},
VOLUME = {135},
YEAR = {2023},
NUMBER = {2},
PAGES = {1111--1130},
URL = {http://www.techscience.com/CMES/v135n2/50150},
ISSN = {1526-1506},
ABSTRACT = {How to accelerate the convergence speed and avoid computing the inversion of a Jacobian matrix is important in the solution of nonlinear algebraic equations (NAEs). This paper develops an approach with a splitting-linearizing technique based on the nonlinear term to reduce the effect of the nonlinear terms. We decompose the nonlinear terms in the NAEs through a splitting parameter and then linearize the NAEs around the values at the previous step to a linear system. Through the maximal orthogonal projection concept, to minimize a merit function within a selected interval of splitting parameters, the optimal parameters can be quickly determined. In each step, a linear system is solved by the Gaussian elimination method, and the whole iteration procedure is convergent very fast. Several numerical tests show the high performance of the optimal split-linearization iterative method (OSLIM).},
DOI = {10.32604/cmes.2022.021655}
}