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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