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We present results about minimization of convex functionals defined over a finite set of vectors in a finite dimensional Hilbert space, that extend several known results for the Benedetto-Fickus frame potential. Our approach depends on majorization techniques. We also consider some perturbation problems, where a positive perturbation of the frame operator… (More)

Given a finite sequence of vectors F 0 in C d we describe the spectral and geometrical structure of optimal frame completions of F 0 obtained by appending a finite sequence of vectors with prescribed norms, where optimality is measured with respect to a general convex potential. In particular, our analysis includes the so-called Mean Square Error (MSE) and… (More)

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