Matrix-free iterative processes with least-squares error damping for nonlinear systems of equations

Журнал Белорусского государственного университета: Математика, информатика

Barys V. Faleichyk¹  Ivan V. Bondar¹ 

[1] Belarusian State University, Niezaliežnasci Avenue, 4, 220030, Minsk, Belarus;

关键词: nonlinear systems of equations;    matrix-free methods;    acceleration of convergence;    least-squares;    newton – krylov method;    difference schemes;   

DOI  :  

来源: DOAJ

【 摘 要 】

New iterative processes for numerical solution of big nonlinear systems of equations are considered. The processes do not require factorization and storing of Jacobi matrix and employ a special technique of convergence acceleration which is called least-squares error damping and requires solution of auxiliary linear least-squares problems of low dimension. In linear case the resulting method is similar to the general minimal residual method (GMRES) with preconditioning. In nonlinear case, in contrast to popular Newton – Krylov method, the computational scheme do not involve operation  of difference approximation of derivative operator. Numerical experiments include three nonlinear problems originating from two-dimensional elliptic partial differential equations and exhibit advantage of the proposed method compared to Newton – Krylov method.

【 授权许可】

Unknown