کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4640111 | 1341261 | 2011 | 9 صفحه PDF | دانلود رایگان |
![عکس صفحه اول مقاله: On the modification of an eigenvalue problem that preserves an eigenspace On the modification of an eigenvalue problem that preserves an eigenspace](/preview/png/4640111.png)
Eigenvalue problems arise in many application areas ranging from computational fluid dynamics to information retrieval. In these fields we are often interested in only a few eigenvalues and corresponding eigenvectors of a sparse matrix. In this paper, we comment on the modifications of the eigenvalue problem that can simplify the computation of those eigenpairs. These transformations allow us to avoid difficulties associated with non-Hermitian eigenvalue problems, such as the lack of reliable non-Hermitian eigenvalue solvers, by mapping them into generalized Hermitian eigenvalue problems. Also, they allow us to expose and explore parallelism. They require knowledge of a selected eigenvalue and preserve its eigenspace. The positive definiteness of the Hermitian part is inherited by the matrices in the generalized Hermitian eigenvalue problem. The position of the selected eigenspace in the ordering of the eigenvalues is also preserved under certain conditions. The effect of using approximate eigenvalues in the transformation is analyzed and numerical experiments are presented.
► We study a technique to make a specific modification of the eigenvalue problem.
► The modification keeps invariant the subspace corresponding to a selected eigenvalue.
► We show how to map non-Hermitian into generalized Hermitian eigenvalue problems.
► We show how to expose and explore parallelism in the eigenvalue problems.
► We study other properties of this transformation.
Journal: Journal of Computational and Applied Mathematics - Volume 235, Issue 18, 15 July 2011, Pages 5432–5440