تقرير
Triangularized Orthogonalization-free Method for Solving Extreme Eigenvalue Problems
| العنوان: | Triangularized Orthogonalization-free Method for Solving Extreme Eigenvalue Problems |
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| المؤلفون: | Gao, Weiguo, Li, Yingzhou, Lu, Bichen |
| سنة النشر: | 2020 |
| المجموعة: | Computer Science Mathematics |
| مصطلحات موضوعية: | Mathematics - Numerical Analysis, 65F15 |
| الوصف: | A novel orthogonalization-free method together with two specific algorithms are proposed to solve extreme eigenvalue problems. On top of gradient-based algorithms, the proposed algorithms modify the multi-column gradient such that earlier columns are decoupled from later ones. Global convergence to eigenvectors instead of eigenspace is guaranteed almost surely. Locally, algorithms converge linearly with convergence rate depending on eigengaps. Momentum acceleration, exact linesearch, and column locking are incorporated to further accelerate both algorithms and reduce their computational costs. We demonstrate the efficiency of both algorithms on several random matrices with different spectrum distribution and matrices from computational chemistry. |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2005.12161 |
| رقم الأكسشن: | edsarx.2005.12161 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |