【摘要】 提出用连续的无导数Landweber方法(或称为无导数动力系统方法)研究Hilbert空间中的参数识别问题。不考虑算子F的Fréchet可微性及其非线性条件,仅在与正演问题可解性相关的某些更为自然的假设条件下,用李雅普诺夫稳定性定理证明该动力系统是收敛且稳定的。在关于算子F更弱的源条件和非线性条件下,推导出相应的离散化后所得迭代方法的收敛率。数值算例验证了所得结论。更多还原

【Abstract】 A continuous derivative-free Landweber method( or called derivative-free dynamical system method) for solving parameter identification problems in Hilbert space setting is proposed. Without the Fréchet differentiability and the nonlinearity conditions of F,by using the theorem of Lyapunov stability,it is proven this dynamical system to be convergent and stable only with more natural assumptions associated with the solvability of a direct problem,and derive the convergent rate of the corresponding iterative method under a weak source condition and a weak nonlinearity condition of F. Finally,some numerical experiments are presented with PC-Matlab to verify the theoretical result.更多还原