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- W2958557968 abstract "We propose a conjugate gradient type optimization technique for the computation of the Karcher mean on the set of complex linear subspaces of fixed dimension, modeled by the so-called Grassmannian. The identification of the Grassmannian with Hermitian projection matrices allows an accessible introduction of the geometric concepts required for an intrinsic conjugate gradient method. In particular, proper definitions of geodesics, parallel transport, and the Riemannian gradient of the Karcher mean function are presented. We provide an efficient step-size selection for the special case of one dimensional complex subspaces and illustrate how the method can be employed for blind identification via numerical experiments." @default.
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- W2958557968 date "2012-09-14" @default.
- W2958557968 modified "2023-10-18" @default.
- W2958557968 title "Averaging Complex Subspaces via a Karcher Mean Approach" @default.
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- W2958557968 doi "https://doi.org/10.48550/arxiv.1209.3197" @default.
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