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

Hongxia Yin; Chen Ling; Liqun Qi

doi:10.1007/s10107-005-0695-z

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

Hongxia Yin, Chen Ling, Liqun Qi

Research output: Journal article publication › Journal article › Academic research › peer-review

4 Citations (Scopus)

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 [InlineMediaObject not available: see fulltext.] where m is the order of the trigonometric bases. This result theoretically confirms the numerical observation by Potter (1990) and Cole and Goodrich (1993).

Original language	English
Pages (from-to)	539-546
Number of pages	8
Journal	Mathematical Programming
Volume	107
Issue number	3
DOIs	https://doi.org/10.1007/s10107-005-0695-z
Publication status	Published - 1 Jul 2006

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Software
Mathematics(all)

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10.1007/s10107-005-0695-z

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AU - Ling, Chen

AU - Qi, Liqun

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N2 - 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 [InlineMediaObject not available: see fulltext.] where m is the order of the trigonometric bases. This result theoretically confirms the numerical observation by Potter (1990) and Cole and Goodrich (1993).

AB - 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 [InlineMediaObject not available: see fulltext.] 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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DO - 10.1007/s10107-005-0695-z

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JO - Mathematical Programming

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

Abstract

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