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Volume 9, Issue 2
The Global Convergence of the GMED Iterative Algorithm

Jin Tang & Cheng-Shu Wang

J. Comp. Math., 9 (1991), pp. 125-134.

Published online: 1991-09

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  • Abstract

In the late 1970's, Wiggins proposed a minimum entropy deconvolution (MED) which has become one of the most important deconvolution methods. He gave a varimax norm $V^4_2$ and a MED iterative procedure. Fortunately, for the last ten years in the practical using, the MED algorithm has never failed to reach a maximizer of the varimax norm. But so far, no theoretical proof has been given to show the convergence of the MED procedure. In this paper, we prove the global convergence of a generalized MED iterative procedure with respect to a generalized varimax norm $V^p_q(q=2,p \gt 2)$.

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@Article{JCM-9-125, author = {Tang , Jin and Wang , Cheng-Shu}, title = {The Global Convergence of the GMED Iterative Algorithm}, journal = {Journal of Computational Mathematics}, year = {1991}, volume = {9}, number = {2}, pages = {125--134}, abstract = {

In the late 1970's, Wiggins proposed a minimum entropy deconvolution (MED) which has become one of the most important deconvolution methods. He gave a varimax norm $V^4_2$ and a MED iterative procedure. Fortunately, for the last ten years in the practical using, the MED algorithm has never failed to reach a maximizer of the varimax norm. But so far, no theoretical proof has been given to show the convergence of the MED procedure. In this paper, we prove the global convergence of a generalized MED iterative procedure with respect to a generalized varimax norm $V^p_q(q=2,p \gt 2)$.

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/9385.html} }
TY - JOUR T1 - The Global Convergence of the GMED Iterative Algorithm AU - Tang , Jin AU - Wang , Cheng-Shu JO - Journal of Computational Mathematics VL - 2 SP - 125 EP - 134 PY - 1991 DA - 1991/09 SN - 9 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/9385.html KW - AB -

In the late 1970's, Wiggins proposed a minimum entropy deconvolution (MED) which has become one of the most important deconvolution methods. He gave a varimax norm $V^4_2$ and a MED iterative procedure. Fortunately, for the last ten years in the practical using, the MED algorithm has never failed to reach a maximizer of the varimax norm. But so far, no theoretical proof has been given to show the convergence of the MED procedure. In this paper, we prove the global convergence of a generalized MED iterative procedure with respect to a generalized varimax norm $V^p_q(q=2,p \gt 2)$.

Tang , Jin and Wang , Cheng-Shu. (1991). The Global Convergence of the GMED Iterative Algorithm. Journal of Computational Mathematics. 9 (2). 125-134. doi:
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