Tensor LU and QR decompositions and their randomized algorithms | ||
| Computational Mathematics and Computer Modeling with Applications (CMCMA) | ||
| مقاله 2، دوره 1، شماره 1، شهریور 2022، صفحه 1-16 اصل مقاله (1.11 M) | ||
| نوع مقاله: Invited paper | ||
| شناسه دیجیتال (DOI): 10.52547/CMCMA.1.1.1 | ||
| نویسندگان | ||
| Yuefeng Zhu1؛ Yimin Wei* 2 | ||
| 1School of Mathematical Sciences, Fudan University, Shanghai, P.R. China | ||
| 2School of Mathematical Sciences and Shanghai Key Laboratory of Contemporary Applied Mathematics, Fudan University, Shanghai, PR China | ||
| چکیده | ||
| In this paper, we propose two decompositions extended from matrices to tensors, including LU and QR decompositions with their rank-revealing and randomized variations. We give the growth order analysis of error of the tensor QR (t-QR) and tensor LU (t-LU) decompositions. Growth order of error and running time are shown by numerical examples. We test our methods by compressing and analyzing the image-based data, showing that the performance of tensor randomized QR decomposition is better than the tensor randomized SVD (t-rSVD) in terms of the accuracy, running time and memory. | ||
| کلیدواژهها | ||
| LU decomposition؛ QR decomposition؛ rank-revealing algorithm؛ randomized algorithm؛ tensor T-product؛ low-rank approximation | ||
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آمار تعداد مشاهده مقاله: 696 تعداد دریافت فایل اصل مقاله: 1,172 |
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