Implementing a New Dense Symmetric Eigensolver on Multicore Systems

الموضوعات

علوم تطبيقية وتكنولوجية

الملخص

We present original advanced architecture implementations of the QDWHeig algo- rithm for solving dense symmetric eigenproblems. The algorithm (Y. Nakatsukasa and N. J. Higham, 2012) performs a spectral divide-and-conquer, which recursively divides the matrix into smaller submatrices by finding an invariant subspace for a subset of the spectrum. The main contribution of this thesis is to enhance the per- formance of QDWHeig algorithm by relying on a high performance kernels from PLASMA [1] and LAPACK [2]. We demonstrate the quality of the eigenpairs that are computed with the QDWHeig algorithm for many matrix types with different eigenvalue clustering. We then implement QDWHeig using kernels from LAPACK and PLASMA, and compare its performance against other divide-and-conquer sym- metric eigensolvers. The main part of QDWHeig is finding a polar decomposition. We introduce mixed precision to enhance the performance in finding the polar decom- position. Our evaluation considers speed and accuracy of the computed eigenvalues. Some applications require finding only a subspectrum of the eigenvalues; therefore we modify the algorithm to find the eigenpairs in a given interval of interest. An ex- perimental study shows significant improvement on the performance of our algorithm using mixed precision and PLASMA routines.

روابط وملفات

التعريف والنوع

رقم الوثيقة

05b7dd03-71f4-41ef-9aef-5b427cc13245

رقم العقد

0

نوع الوسائط

Crawler

نوع المحتوى

الرسائل العلمية

صيغة المصدر

رسائل ماجيستير

نوع الملف

pdf text

أسماء الملفات

1700503_1.pdf

بيانات النشر

ألقاب المؤلفين

[{"name_ar":"دلال عرسان السكري","title_ar":"اعداد","title_en":"Preparation"},{"name_ar":"ديفيد كيز","title_ar":"اشراف","title_en":"Supervision"}]

اللغة

English

المصدر والدورية

اسم المصدر

Implementing a New Dense Symmetric Eigensolver on Multicore Systems

المحتوى والصفحات

عدد الصفحات

0

كلمات الباحثين

accuracy, eigensolver , implementation , lapack , performance , plasma

إشراف وإعداد

الإشراف

ديفيد كيز

الإعداد

دلال عرسان السكري

الاقتباسات الببليوغرافية