کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4602583 1336930 2008 18 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Approximation of the joint spectral radius using sum of squares
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
Approximation of the joint spectral radius using sum of squares
چکیده انگلیسی

We provide an asymptotically tight, computationally efficient approximation of the joint spectral radius of a set of matrices using sum of squares (SOS) programming. The approach is based on a search for an SOS polynomial that proves simultaneous contractibility of a finite set of matrices. We provide a bound on the quality of the approximation that unifies several earlier results and is independent of the number of matrices. Additionally, we present a comparison between our approximation scheme and earlier techniques, including the use of common quadratic Lyapunov functions and a method based on matrix liftings. Theoretical results and numerical investigations show that our approach yields tighter approximations.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Linear Algebra and its Applications - Volume 428, Issue 10, 1 May 2008, Pages 2385-2402