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arXiv · 1201.0101

The geometric mean of two matrices from a computational viewpoint

Bruno Iannazzo
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Abstract

The geometric mean of two matrices is considered and analyzed from a computational viewpoint. Some useful theoretical properties are derived and an analysis of the conditioning is performed. Several numerical algorithms based on different properties and representation of the geometric mean are discussed and analyzed and it is shown that most of them can be classified in terms of the rational approximations of the inverse square root functions. A review of the relevant applications is given.

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Bruno Iannazzo. 2011-12-30. The geometric mean of two matrices from a computational viewpoint. https://arxiv.org/abs/1201.0101

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