کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4599264 1631126 2015 30 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Multiplicative Lidskii's inequalities and optimal perturbations of frames
ترجمه فارسی عنوان
نابرابری لیدسکای چند ضلعی و اختلالات بهینه فریم ها؟
کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
چکیده انگلیسی

In this paper we study two design problems in frame theory: on the one hand, given a fixed finite frame F={fj}j∈InF={fj}j∈In for CdCd we compute those dual frames GG of FF that are optimal perturbations of the canonical dual frame for FF under certain restrictions on the norms of the elements of GG. On the other hand, we compute those V⋅F={Vfj}j∈InV⋅F={Vfj}j∈In – for invertible operators V   which are close to the identity – that are optimal perturbations of FF. That is, we compute the optimal perturbations of FF among frames G={gj}j∈InG={gj}j∈In that have the same linear relations as FF. In both cases, optimality is measured with respect to submajorization of the eigenvalues of the frame operators. Hence, our optimal designs are minimizers of a family of convex potentials that include the frame potential and the mean squared error. The key tool for these results is a multiplicative analogue of Lidskii's inequality in terms of log-majorization and a characterization of the case of equality.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Linear Algebra and its Applications - Volume 469, 15 March 2015, Pages 539–568
نویسندگان
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