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Volume 30, Issue 4
Solving the Backward Heat Conduction Problem by Data Fitting with Multiple Regularizing Parameters

Qun Chen & Jijun Liu

DOI: 10.4208/jcm.1111-m3457

J. Comp. Math., 30 (2012), pp. 418-432.

Published online: 2012-08

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  • Abstract

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.

  • Keywords

Inverse problem, Data fitting, Regularization, Convergence rate, Numerics.

  • AMS Subject Headings

34L16, 35K05, 41A25, 65F22.

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JCM-30-418, author = {Qun Chen and Jijun Liu}, title = {Solving the Backward Heat Conduction Problem by Data Fitting with Multiple Regularizing Parameters}, journal = {Journal of Computational Mathematics}, year = {2012}, volume = {30}, number = {4}, pages = {418--432}, abstract = {

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.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1111-m3457}, url = {http://global-sci.org/intro/article_detail/jcm/8440.html} }
TY - JOUR T1 - Solving the Backward Heat Conduction Problem by Data Fitting with Multiple Regularizing Parameters AU - Qun Chen & Jijun Liu JO - Journal of Computational Mathematics VL - 4 SP - 418 EP - 432 PY - 2012 DA - 2012/08 SN - 30 DO - http://doi.org/10.4208/jcm.1111-m3457 UR - https://global-sci.org/intro/article_detail/jcm/8440.html KW - Inverse problem, Data fitting, Regularization, Convergence rate, Numerics. AB -

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.

Qun Chen and Jijun Liu. (2012). Solving the Backward Heat Conduction Problem by Data Fitting with Multiple Regularizing Parameters. Journal of Computational Mathematics. 30 (4). 418-432. doi:10.4208/jcm.1111-m3457
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