کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4643457 1632059 2006 20 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Bounds on the eigenvalue range and on the field of values of non-Hermitian and indefinite finite element matrices
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات کاربردی
پیش نمایش صفحه اول مقاله
Bounds on the eigenvalue range and on the field of values of non-Hermitian and indefinite finite element matrices
چکیده انگلیسی

In the early seventies, Fried formulated bounds on the spectrum of assembled Hermitian positive (semi-) definite finite element matrices using the extreme eigenvalues of the element matrices. In this paper we will generalise these results by presenting bounds on the field of values, the numerical radius and on the spectrum of general, possibly complex matrices, for both the standard and the generalised problem. The bounds are cheap to compute, involving operations with element matrices only. We illustrate our results with an example from acoustics involving a complex, non-Hermitian matrix. As an application, we show how our estimates can be used to derive an upper bound on the number of iterations needed to achieve a given residual reduction in the GMRES-algorithm for solving linear systems.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Computational and Applied Mathematics - Volume 189, Issues 1–2, 1 May 2006, Pages 304–323
نویسندگان
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