A mixed Newton-Tikhonov method for nonlinear ill-posed problems

作者：Kang Chuan gang; He Guo qiang^*

来源：Applied Mathematics and Mechanics (English Edition ), 2009, 30(6): 741-752.

DOI：10.1007/s10483-009-0608-2

• nonlinear ill-posed problem
• inverse heat conduction problem
• mixed Newton-Tikhonov method
• convergence
• stability

Newton type methods are one kind of the efficient methods to solve nonlinear ill-posed problems, which have attracted extensive attention. However, computational cost of Newton type methods is high because practical problems are complicated. We propose a mixed Newton-Tikhonov method, i.e., one step Newton-Tikhonov method with several other steps of simplified Newton-Tikhonov method. Convergence and stability of this method are proved under some conditions. Numerical experiments show that the proposed method has obvious advantages over the classical Newton method in terms of computational costs.

• 出版日期2009-6
• 单位上海大学