A Newton type iterative inverse method for heat-conduction problems

An inverse problem for identification of the coefficient in heat-conduction equation is considered. After reducing the problem to a nonlinear ill-posed operator equation, Newton type iterative methods are considered. The implicit iterative method is applied to the linearized Newton equation, and the key step in the process is that a new reasonable a posteriori stopping rule for the inner iteration is presented. Numerical experiments for the new method as well as for Tikhonov method and Bakushikskii method are given, and these results show the obvious advantages of the new method over the other ones.     

求解非光滑方程组的Newton-GMRES方法的全局收敛性分析

1引言对于非光滑方程组F(y)=0(1.1)的求解,这里F:D(?)R~n→R~n是一个非光滑映射,目前主要有两种求解方法.一种方法是由Pang提出的.     

解非光滑方程组的Krylov子空间迭代法

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．     

求解热传导反问题的一种正则化Newton型迭代法

讨论热传导方程求解系数的一个反问题．把问题归结为一个非线性不适定的算子方程后,考虑该方程的Newton型迭代方法．对线性化后的Newton方程用隐式迭代法求解,关键的一步是引入了一种新的更合理的确定(内)迭代步数的后验准则．对新方法及对照的Tikhonov方法和Bakushiskii方法进行了数值实验,结果显示了新方法具有明显的优越性．     

A Newton type iterative method for heat-conduction inverse problems

An inverse problem for identification of the coefficient in heat-conduction equation is considered. After reducing the problem to a nonlinear ill-posed operator equation, Newton type iterative methods are considered. The implicit iterative method is applied to the linearized Newton equation, and the key step in the process is that a new reasonable a posteriori stopping rule for the inner iteration is presented. Numerical experiments for the new method as well as for Tikhonov method and Bakushikskii method are given, and these results show the obvious advantages of the new method over the other ones.     

求解椭圆方程柯西问题的修正吉洪诺夫正则化方法

研究了一类变系数椭圆方程的柯西问题,这类问题出现在很多实际问题领域.由于问题的不适定性,不可能通过经典的数值方法来求解上述问题,必须引入正则化手段.采用了一种修正吉洪诺夫正则化方法来求解上述问题.在一种先验和一种后验参数选取准则下,分别获得了问题的误差估计.数值例子进一步显示方法是稳定有效的.     

Nonlinear Krylov subspace methods for solving nonsmooth equations

IntroductionConsider the nonsmooth equationsF(y)=0,(1)whereF:D Rn→Rn.In1993,Qi and Sun[1]proposed the generalized Newton method forsolving Eq.(1)yk 1=yk-Vk-1F(yk),(2)whereVk∈F(yk)is the generalized Jacobi matrixofF[2],F(y)=Co{lyii→myyi∈DF F(yi)},andpr…