کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4602229 1631168 2008 21 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Algorithms for multidimensional spectral factorization and sum of squares
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
Algorithms for multidimensional spectral factorization and sum of squares
چکیده انگلیسی

In this paper, algorithms are developed for the problems of spectral factorization and sum of squares of polynomial matrices with n indeterminates, and a natural interpretation of the tools employed in the algorithms is given using ideas from the theory of lossless and dissipative systems. These algorithms are based on the calculus of 2n-variable polynomial matrices and their associated quadratic differential forms, and share the common feature that the problems are lifted from the original n-variable polynomial context to a 2n-variable polynomial context. This allows to reduce the spectral factorization problem and the sum of squares problem to linear matrix inequalities (LMI’s), to the feasibility of a semialgebraic set or to a linear eigenvalue problem.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Linear Algebra and its Applications - Volume 429, Issues 5–6, 1 September 2008, Pages 1114-1134