|Title:||Nonlinear Algebraic Equations Solved by an Optimal Splitting-Linearizing Iterative Method||Authors:||Liu, Chein-Shan
El-Zahar, Essam R.
|Keywords:||Nonlinear algebraic equations;novel splitting-linearizing technique;iterative method;maximal projection;optimal splitting parameter||Issue Date:||1-Jan-2023||Publisher:||TECH SCIENCE PRESS||Journal Volume:||135||Journal Issue:||2||Start page/Pages:||1111-1130||Source:||CMES-COMPUTER MODELING IN ENGINEERING & SCIENCES||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).
|Appears in Collections:||海洋中心|
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.