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A Posteriori Fractional Tikhonov Regularization Method for the Problem of Analytic Continuation

Author

Listed:
  • Xuemin Xue

    (Department of Mathematics, Northwest Normal University, Lanzhou 730070, China)

  • Xiangtuan Xiong

    (Department of Mathematics, Northwest Normal University, Lanzhou 730070, China)

Abstract

In this paper, the numerical analytic continuation problem is addressed and a fractional Tikhonov regularization method is proposed. The fractional Tikhonov regularization not only overcomes the difficulty of analyzing the ill-posedness of the continuation problem but also obtains a more accurate numerical result for the discontinuity of solution. This article mainly discusses the a posteriori parameter selection rules of the fractional Tikhonov regularization method, and an error estimate is given. Furthermore, numerical results show that the proposed method works effectively.

Suggested Citation

  • Xuemin Xue & Xiangtuan Xiong, 2021. "A Posteriori Fractional Tikhonov Regularization Method for the Problem of Analytic Continuation," Mathematics, MDPI, vol. 9(18), pages 1-11, September.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:18:p:2255-:d:635162
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    References listed on IDEAS

    as
    1. Xiong, Xiangtuan & Zhu, Liqin & Li, Ming, 2011. "Regularization methods for a problem of analytic continuation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 82(2), pages 332-345.
    2. Deng, Zhi-Liang & Fu, Chu-Li & Feng, Xiao-Li & Zhang, Yuan-Xiang, 2011. "A mollification regularization method for stable analytic continuation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(8), pages 1593-1608.
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