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- W1980984606 abstract "In this paper we consider a family of nonlinear matrix equations based on the higher-order geometric means of positive definite matrices that proposed by Ando–Li–Mathias. We prove that the geometric mean equation X = B + G ( A 1 , A 2 , … , A m , X , X , … , X ︸ n ) has a unique positive definite solution depending continuously on the parameters of positive definite A i and positive semidefinite B . It is shown that the unique positive definite solutions G n ( A 1 , A 2 , … , A m ) for B = 0 satisfy the minimum properties of geometric means, yielding a sequence of higher-order geometric means of positive definite matrices." @default.
- W1980984606 created "2016-06-24" @default.
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- W1980984606 date "2008-04-01" @default.
- W1980984606 modified "2023-09-28" @default.
- W1980984606 title "On Ando–Li–Mathias geometric mean equations" @default.
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- W1980984606 doi "https://doi.org/10.1016/j.laa.2007.10.027" @default.
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