论文信息 - Convergence and uniqueness properties of Gauss-Newton's method

Convergence and uniqueness properties of Gauss-Newton's method

Abstract The generalized radius and center Lipschitz conditions with L average are introduced to investigate the convergence of Gauss-Newton's method for finding the nonlinear least squares solution of nonlinear equations. The radii of the convergence ball of Gauss-Newton's method and the uniqueness ball of the solution are estimated. Some applications are given.

[1] G. Stewart. On the Continuity of the Generalized Inverse , 1969 .

[2] K. S. Banerjee. Generalized Inverse of Matrices and Its Applications , 1973 .

[3] Henryk Wozniakowski,et al. Convergence and Complexity of Newton Iteration for Operator Equations , 1979, JACM.

[4] Chong Li,et al. Convergence of Newton's Method and Uniqueness of the Solution of Equations in Banach Spaces II , 2003 .

[5] Ya-Xiang Yuan,et al. Optimization theory and methods , 2006 .

[6] P. Wedin. Perturbation theory for pseudo-inverses , 1973 .

[7] Xinghua Wang,et al. Convergence of Newton's method and uniqueness of the solution of equations in Banach space , 2000 .

[8] S. Smale. Newton’s Method Estimates from Data at One Point , 1986 .