کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4598698 1631099 2016 18 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
A fixed point mean approximation to the Cartan barycenter of positive definite matrices
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
A fixed point mean approximation to the Cartan barycenter of positive definite matrices
چکیده انگلیسی

In this paper we define a new weighted inductive geometric mean HnHn on the Riemannian manifold of positive definite matrices of fixed size and present its fixed point mean approximation to the Cartan barycenter (Karcher mean). We show that for t∈(0,1]t∈(0,1], the weighted geometric mean equation X=Hn+1(ωt;A1,…,An,X)X=Hn+1(ωt;A1,…,An,X), where ωt=t1+t(w1,…,wn,1/t), has a unique positive definite solution that approaches as t→0+t→0+ to the ω  -weighted Cartan mean of A1,…,AnA1,…,An. Numerical computations for the stochastic convergence in terms of HnHn to derive a new contractive barycenter other than the Cartan barycenter are presented.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Linear Algebra and its Applications - Volume 496, 1 May 2016, Pages 420–437
نویسندگان
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