Solving the Backward Heat Conduction Problem by Data Fitting with Multiple Regularizing Parameters

Qun Chen and Jijun Liu

Type: Article

Publication Date: 2012-06-01

Citations: 11

DOI: https://doi.org/10.4208/jcm.1111-m3457

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.

Locations

Journal of Computational Mathematics - View - PDF

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Works Cited by This (20)

Action	Title	Year	Authors
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+ PDF Chat	Inverse Problems for Partial Differential Equations	1998	Victor Isakov
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+	A quasi Tikhonov regularization for a two-dimensional backward heat problem by a fundamental solution	2008	Jin Cheng J J Liu
+	New model function methods for determining regularization parameters in linear inverse problems	2009	Zewen Wang Jijun Liu