کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4599578 1631141 2014 23 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
On expansion of search subspaces for large non-Hermitian eigenproblems
کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
On expansion of search subspaces for large non-Hermitian eigenproblems
چکیده انگلیسی

How to expand a given subspace efficiently is an important task for large sparse eigenvalue problems. In this paper, we are interested in the following question: which vector from a given subspace, after multiplied by the matrix A, will give a better expanded search subspace. In (2008) [33], Ye investigated this problem and determined how to choose the optimal expansion vector theoretically. Unfortunately, the result is not computable since it involves some unknown information on the desired eigenvector. When A is symmetric, it was suggested that the Ritz vector may lead to a good candidate for subspace expansion. However, when A is non-Hermitian, the Ritz vector may not be a satisfactory choice. The contribution of this paper is twofold. First, we suggest to use the refined Ritz vector to expand the search subspace, and propose a residual expansion Arnoldi method for subspace expansion. Theoretical results justify the use of the refined Ritz vector. Second, we prove that the elements of the primitive refined Ritz vector have a decreasing pattern going to zero. We then show that the decreasing pattern exists in an arbitrary primitive approximate eigenvector, and derive an inexact residual expansion Arnoldi method for subspace expansion. Numerical examples show the effectiveness of our theoretical results and illustrate the numerical behavior of the new method for subspace expansion.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Linear Algebra and its Applications - Volume 454, 1 August 2014, Pages 107–129
نویسندگان
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