کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
5773328 1631064 2017 19 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
The inverse q-numerical range problem and connections to the Davis-Wielandt shell and the pseudospectra of a matrix
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
The inverse q-numerical range problem and connections to the Davis-Wielandt shell and the pseudospectra of a matrix
چکیده انگلیسی
Numerical ranges and related sets provide insights into the behavior of algorithms involving matrices, and inverse numerical range problems attempt to enhance these insights. We generalize the inverse numerical range problem, as proposed by Uhlig, to the inverse q-numerical range problem, and propose an algorithm for solving the problem that relies on convexity. To determine an approximation to the boundary of the q-numerical range, as needed by our algorithm, we must approximate the top of the Davis-Wielandt shell, a generalization of the numerical range. We found that the Davis-Wielandt shell is in a sense conjugate to the extreme singular values of the resolvent of a matrix. Knowing the Davis-Wielandt shell allows for the approximation of the q-numerical range, the pseudospectra and the Davis-Wielandt shell for any allowed Möbius transformation of a matrix. We provide some examples illustrating these connections, as well as how to solve the inverse q-numerical range problem.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Linear Algebra and its Applications - Volume 531, 15 October 2017, Pages 479-497
نویسندگان
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