Global convergence of triangularized orthogonalization-free method
| العنوان: | Global convergence of triangularized orthogonalization-free method |
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| المؤلفون: | Gao, Weiguo, Li, Yingzhou, Lu, Bichen |
| المصدر: | Communications in Mathematical Sciences. 21:195-218 |
| بيانات النشر: | International Press of Boston, 2023. |
| سنة النشر: | 2023 |
| مصطلحات موضوعية: | 65F15, Applied Mathematics, General Mathematics, FOS: Mathematics, Numerical Analysis (math.NA), Mathematics - Numerical Analysis |
| الوصف: | This paper proves the global convergence of a triangularized orthogonalization-free method (TriOFM). TriOFM, in general, applies a triangularization idea to the gradient of an objective function and removes the rotation invariance in minimizers. More precisely, in this paper, the TriOFM works as an eigensolver for sizeable sparse matrices and obtains eigenvectors without any orthogonalization step. Due to the triangularization, the iteration is a discrete-time flow in a non-conservative vector field. The global convergence relies on the stable manifold theorem, whereas the convergence to stationary points is proved in detail in this paper. We provide two proofs inspired by the noisy power method and the noisy optimization method, respectively. |
| تدمد: | 1945-0796 1539-6746 |
| URL الوصول: | https://explore.openaire.eu/search/publication?articleId=doi_dedup___::53ca82c2113b76be104507abaee544a6 https://doi.org/10.4310/cms.2023.v21.n1.a9 |
| حقوق: | OPEN |
| رقم الأكسشن: | edsair.doi.dedup.....53ca82c2113b76be104507abaee544a6 |
| قاعدة البيانات: | OpenAIRE |
| تدمد: | 19450796 15396746 |
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