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

I. V. Bondar ; B. V. Faleichik

Journal of the Belarusian State University. Mathematics and Informatics, Tome 3 (2017), pp. 73-84

Résumé

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.

Détail

Keywords: nonlinear systems of equations; matrix-free methods; acceleration of convergence; least-squares; Newton – Krylov method; difference schemes.