Constructing matrix geometric means
نویسنده
چکیده
In this paper, we analyze the process of “assembling” new matrix geometric means from existing ones, and show what new means can be found, and what cannot be done because of group-theoretical obstructions. We show that for n = 4 a new matrix mean exists which is simpler to compute than the existing ones. Moreover, we show that for n > 4 the existing strategies of composing matrix means and taking limits of iterations cannot provide a mean computationally simpler than the existing ones.
منابع مشابه
Ela Constructing Matrix Geometric Means
In this paper, we analyze the process of “assembling” new matrix geometric means from existing ones, through function composition or limit processes. We show that for n = 4 a new matrix mean exists which is simpler to compute than the existing ones. Moreover, we show that for n > 4 the existing proving strategies cannot provide a mean computationally simpler than the existing ones.
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