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Numerical pseudodifferential operator and Fourier regularization

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Abstract

The concept of numerical pseudodifferential operator, which is an extension of numerical differentiation, is suggested. Numerical pseudodifferential operator just is calculating the value of the pseudodifferential operator with unbounded symbol. Many ill-posed problems can lead to numerical pseudodifferential operators. Fourier regularization is a very simple and effective method for recovering the stability of numerical pseudodifferential operators. A systematically theoretical analysis and some concrete examples are provided.

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Author information

Authors and Affiliations

  1. School of Mathematics and Statistics, Lanzhou University, Lanzhou, 730000, People’s Republic of China

    Chu-Li Fu & Zhi Qian

  2. Department of Mathematics, Nanjing University, Nanjing, 210093, People’s Republic of China

    Zhi Qian

Authors
  1. Chu-Li Fu
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  2. Zhi Qian
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Corresponding author

Correspondence to Chu-Li Fu.

Additional information

Communicated by the guest editors Benny Hon, Jin Cheng and Masahiro Yamamoto.

The work described in this paper was supported by the NSF of China (10671085) and China Postdoctoral Science Foundation funded project (No.20080440157).

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Fu, CL., Qian, Z. Numerical pseudodifferential operator and Fourier regularization. Adv Comput Math 33, 449–470 (2010). https://doi.org/10.1007/s10444-009-9136-5

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  • DOI: https://doi.org/10.1007/s10444-009-9136-5

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