http://chineseinput.net/에서 pinyin(병음)방식으로 중국어를 변환할 수 있습니다.
변환된 중국어를 복사하여 사용하시면 됩니다.
A new proof to construct multivariable geometric means by symmetrization
김세정,DENES PETZ 한국전산응용수학회 2015 Journal of applied mathematics & informatics Vol.33 No.3
The original geometric mean of two positive definite operators $A$ and $B$ is given by \begin{displaymath} \displaystyle A \# B = A^{1/2} (A^{-1/2} B A^{-1/2})^{1/2} A^{1/2}. \end{displaymath} In this article we provide a new proof to construct from the two-variable geometric mean to the multivariable mean via symmetrization introduced by Lawson and Lim \cite{LL1}. Finally we provide an algorithm to find three-variable geometric mean via symmetrization, which plays an important role to construct higher-order geometric means.
A NEW PROOF TO CONSTRUCT MULTIVARIABLE GEOMETRIC MEANS BY SYMMETRIZATION<xref>†</xref>
KIM, SEJONG,PETZ, DENES The Korean Society for Computational and Applied M 2015 Journal of applied mathematics & informatics Vol.33 No.3
The original geometric mean of two positive definite operators A and B is given by <italic>A</italic>#<italic>B</italic> = <italic>A</italic><sup>1/2</sup>(<italic>A</italic><sup>-1/2</sup><italic>BA</italic><sup>-1/2</sup>)<sup>1/2</sup><italic>A</italic><sup>1/2</sup>. In this article we provide a new proof to construct from the two-variable geometric mean to the multivariable mean via symmetrization introduced by Lawson and Lim [5]. Finally we provide an algorithm to find three-variable geometric mean via symmetrization, which plays an important role to construct higher-order geometric means.