求解非线性不适定的混合Newton-Tikhonov迭代法

A Mixed Newton-Tikhonov Method for Nonlinear Ill-Posed Problems

鉴于Newton型方法在实际计算中计算量可能非常大,因此提出了一种一步Newton结合若干步简化Newton的混合Newton-Tikhonov方法,并且在一定条件下证明了该方法的收敛性和稳定性.数值试验表明,在减少计算量方面该方法相对于经典的Newton方法有明显的改善.

Newton type methods are one kind of the efficient methods to solve nonlinear ill-posed problems and attract extensive attention of people. However, the computational cost of Newton type methods may be very large because of the complexity of practical problems. A mixed Newton- Tikhonov method,i, e. ,one step Newton-Tikhonov method with several other steps of simplified Newton-Tikhonov method was proposed. The convergence and stability of this method were proved under some conditions. Numerical experiments show that the new method has obvious improvement over the classical Newton method in the reduction of the computational cost.