SOLVING THE BACKWARD HEAT CONDUCTION PROBLEM BY DATA FITTING WITH MULTIPLE REGULARIZING PARAMETERS  

作　　者：Qun Chen Jijun Liu 

机构地区：[1]Department of Mathematics,Southeast University,Nanjing 210096,China College of Mathematics and Statistics,Nanjing University of Information Science and Technology,Nanjing 210044,China [2]Department of Mathematics,Southeast University,Nanjing 210096,China

出　　处：《Journal of Computational Mathematics》2012年第4期418-432,共15页计算数学（英文）

基　　金：Acknowledgments. This work is supported by NSFC （No.11071039） and Natural Science Foundation of Jiangsu Province （No.BK2011584）.

摘　　要：We propose a new reconstruction scheme for the backward heat conduction problem. By using the eigenfunction expansions, this ill-posed problem is solved by an optimization problem, which is essentially a regularizing scheme for the noisy input data with both the number of truncation terms and the approximation accuracy for the final data as multiple regularizing parameters. The convergence rate analysis depending on the strategy of choosing regularizing parameters as well as the computational accuracy of eigenfunctions is given. Numerical implementations are presented to show the validity of this new scheme.We propose a new reconstruction scheme for the backward heat conduction problem. By using the eigenfunction expansions, this ill-posed problem is solved by an optimization problem, which is essentially a regularizing scheme for the noisy input data with both the number of truncation terms and the approximation accuracy for the final data as multiple regularizing parameters. The convergence rate analysis depending on the strategy of choosing regularizing parameters as well as the computational accuracy of eigenfunctions is given. Numerical implementations are presented to show the validity of this new scheme.

关 键 词：Inverse problem Data fitting REGULARIZATION Convergence rate Numerics. 

分 类 号：O551.3[理学—热学与物质分子运动论] O241.5[理学—物理]