具优势对称部分的非对称非线性问题的不精确Newton分裂算法

本文讨论了处理具优势对称部分的非对称非线性问题的不精确Newton方法.利用矩阵分裂技术,建立了求解此类问题的一类不精确Newton分裂极小参量法、不精确Newton分裂对称LQ法(简记:Newton-SMINRES,Newton-SSYMMLQ),并在合理的假设下,证明了算法的收敛性.数值计算表明:Newton-SMINRES,Newton-SSYMMLQ算法的收敛行为要好于一般求解非线性方程组的Newton-Krylov子空间方法:Newton-BiCGSTAB,Newton-GMRES和Newton-MINRES等算法.

INEXACT NEWTON-SPLITTING METHODS FOR NON-SYMMETRIC NONLINEAR PROBLEMS WITH A DOMINANT SYMMETRIC PART

Inexact Newton-Krylov subspace methods for the non-symmetric problems with a dominant symmetric part are studied in this paper. For the non-symmetric problems with a dominant symmetric part, a class of inexact Newton-splitting methods:Newton-splitting minimal residual method, Newton-splitting symmetric LQ method(denoted briefly by Newton-SMINRES, Newton-SSYMMLQ)are presented by making use of the matrix splitting technique. Under reasonable hypotheses, the convergence of these methods is proved. Numerical computations show that numerical behaviors of the Newton-SMINRES method, Newton-SSYMMLQ method are superior to those of some standard Newton-Krylov subspace methods such as Newton-BiCGSTAB, Newton-GMRES and Newton-MINRES etc..