Nonlinear Krylov Subspace Methods for Solving Nonsmooth Equations
-
摘要: 给出了求解非光滑方程组的Newton-FOM算法和Newton-GMRES算法，证明了这些Krylov子空间方法的局部平方收敛性．数值结果表明了算法的有效性．
-
关键词:
- 非光滑方程组 /
- Newton-FOM算法 /
- Newton-GMRES算法
Abstract: Newton-FOM algorithm and Newton-GMRES algorithm for solving nonsmooth equations are presented.It is proved that these Krylov subspace algorithms have locally quadratic convergence.Numerical experiments demonstrate the effectiveness of the algorithms.-
Key words:
- nonsmooth equations /
- Newton-FOM algorithm /
- Newton-GMRES algorithm
-
[1] QI Li-qun,SUN Ji-e.A nonsmooth version of Newton's method[J].Mathematical Programming,1993,58(3):353—367. doi: 10.1007/BF01581275 [2] Clarke Frank H.Optimization and Nonsmooth Analysis[M].New York:Wiley,1983,69—70. [3] Harker Patrick T,XIAO Bai-chun.Newton's method for the nonlinear complementarity problem:a B-differentiable equation approach[J].Mathematical Progamming,1990,48(3):339—357. doi: 10.1007/BF01582262 [4] IP Chi-ming,Kyparisis Jerzy.Local convergence of quasi-Newton methods for B-differentiable equations[J].Mathematical Progamming,1992,56(1):71—89. doi: 10.1007/BF01580895 [5] Martinez José mario,QI Li-qun.Inexact Newton methods for solving nonsmooth equations[J].Journal of Computational and Applied Mathematics,1995,60(1/2):127—145. doi: 10.1016/0377-0427(94)00088-I [6] PANG Jong-shi,QI Li-qun.Nonsmooth equations: motivation and algorithms[J].SIAM Journal on Optimization,1993,3(2):443—465. doi: 10.1137/0803021 [7] PANG Jong-shi.Newton's method for B-differentiable equations[J].Mathematical of Operations Research,1990,15(2):311—341. doi: 10.1287/moor.15.2.311 [8] QI Li-qun.Convergence analysis of some algorithms for solving nonsmooth equations[J].Mathematical of Operations Research,1993,18(1):227—244. doi: 10.1287/moor.18.1.227 [9] Brown Peter N.Local convergence theory for combined inexact Newton/finite-difference projection methods[J].SIAM Journal on Numerical Analysis,1987,24(2):407—433. doi: 10.1137/0724031 [10] Brown Peter N,Saad Youcef.Convergence theory of nonlinear Newton-Krylov algorithms[J].SIAM Journal on Optimization,1994,4(2):297—330. doi: 10.1137/0804017 [11] Brown Peter N,Saad Youcef.Hybrid Krylov methods for nonlinear systems of equations[J].SIAM Journal on Scientific Computing,1990,11(3):450—481. doi: 10.1137/0911026 -
计量
- 文章访问数: 2549
- HTML全文浏览量: 144
- PDF下载量: 872
- 被引次数: 0
下载:
渝公网安备50010802005915号