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Discretized Tikhonov regularization by reproducing kernel Hilbert space for backward heat conduction problem

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Abstract

In this paper we propose a numerical reconstruction method for solving a backward heat conduction problem. Based on the idea of reproducing kernel approximation, we reconstruct the unknown initial heat distribution from a finite set of scattered measurement of transient temperature at a fixed final time. Standard Tikhonov regularization technique using the norm of reproducing kernel is adopt to provide a stable solution when the measurement data contain noises. Numerical results indicate that the proposed method is stable, efficient, and accurate.

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Authors and Affiliations

  1. Department of Mathematics, City University of Hong Kong, Hong Kong SAR, People’s Republic of China

    Y. C. Hon

  2. Center for Research in Scientific Computation, North Carolina State University, Raleigh, NC, USA

    Tomoya Takeuchi

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  1. Y. C. Hon
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  2. Tomoya Takeuchi
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Correspondence to Y. C. Hon.

Additional information

Communicated by Charles A. Micchelli.

The work described in this paper was fully supported by a grant from the Research Grants Council of the Hong Kong Special Administrative Region, China (Project No. CityU 101209).

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Hon, Y.C., Takeuchi, T. Discretized Tikhonov regularization by reproducing kernel Hilbert space for backward heat conduction problem. Adv Comput Math 34, 167–183 (2011). https://doi.org/10.1007/s10444-010-9148-1

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  • DOI: https://doi.org/10.1007/s10444-010-9148-1

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