Convergence rate of Newton's method for L2 spectral estimation

• 成果类型: Article
• 署名作者: Yin, HX; Ling, C; Qi, LQ
• 署名单位: Chinese Academy of Sciences; University of Chinese Academy of Sciences, CAS; Zhejiang University of Finance & Economics; Hong Kong Polytechnic University
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-005-0695-z
• 发表日期: 2006
• 页码: 539-546
• 关键词: convex subset; Dual approach; interpolation; semismoothness; EQUATIONS

摘要

In the paper, we prove the Holder 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 1 + 2/2m, where m is the order of the trigonometric bases. This result theoretically confirms the numerical observation by Potter (1990) and Cole and Goodrich (1993).