کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
524670 868818 2011 12 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Parallel solution of partial symmetric eigenvalue problems from electronic structure calculations
موضوعات مرتبط
مهندسی و علوم پایه مهندسی کامپیوتر نرم افزارهای علوم کامپیوتر
پیش نمایش صفحه اول مقاله
Parallel solution of partial symmetric eigenvalue problems from electronic structure calculations
چکیده انگلیسی

The computation of selected eigenvalues and eigenvectors of a symmetric (Hermitian) matrix is an important subtask in many contexts, for example in electronic structure calculations. If a significant portion of the eigensystem is required then typically direct eigensolvers are used. The central three steps are: reduce the matrix to tridiagonal form, compute the eigenpairs of the tridiagonal matrix, and transform the eigenvectors back. To better utilize memory hierarchies, the reduction may be effected in two stages: full to banded, and banded to tridiagonal. Then the back transformation of the eigenvectors also involves two stages. For large problems, the eigensystem calculations can be the computational bottleneck, in particular with large numbers of processors. In this paper we discuss variants of the tridiagonal-to-banded back transformation, improving the parallel efficiency for large numbers of processors as well as the per-processor utilization. We also modify the divide-and-conquer algorithm for symmetric tridiagonal matrices such that it can compute a subset of the eigenpairs at reduced cost. The effectiveness of our modifications is demonstrated with numerical experiments.


► Two-step tridiagonal reduction/back transformation shows better scalability.
► Kernels for blocked Householder transformations improve performance.
► Savings in divide-and-conquer method for partial eigensystem.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Parallel Computing - Volume 37, Issue 12, December 2011, Pages 783–794
نویسندگان
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