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Convergence rate of Newton's method for L 2 spectral estimation

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Abstract

In the paper, we prove the Hölder continuous property of the Jacobian of the function generated from the dual of the power spectrum estimation problem. It follows that the convergence of the Newton method for the problem is at least of order where m is the order of the trigonometric bases. This result theoretically confirms the numerical observation by Potter (1990) and Cole and Goodrich (1993).

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Author notes

  1. Chen Ling

    Present address: Department of Applied Mathematics, The Hong Kong Polytechnic University, Kowloon, Hong Kong

Authors and Affiliations

  1. Chinese Academy of Sciences Research Center on Data Technology and Knowledge Economy, Department of Mathematics, Graduate University of the Chinese Academy of Sciences, Beijing, 100049, China

    Hongxia Yin

  2. School of Information, Zhejiang University of Finance and Economics, Hangzhou, 310012, China

    Chen Ling

  3. Department of Applied Mathematics, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong

    Liqun Qi

Authors
  1. Hongxia Yin
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  2. Chen Ling
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  3. Liqun Qi
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Corresponding author

Correspondence to Liqun Qi.

Additional information

This author's work was partially supported by the Hong Kong Research Grant Council and the National Natural Science Foundation of China NSF70472074.

This author's work is supported by the Hong Kong Research Grant Council.

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Yin, H., Ling, C. & Qi, L. Convergence rate of Newton's method for L 2 spectral estimation. Math. Program. 107, 539–546 (2006). https://doi.org/10.1007/s10107-005-0695-z

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