Maximum relative distance between real rank-two and rank-one tensors
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| Định dạng: | Sách |
| Ngôn ngữ: | English |
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Springer
2023
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| Truy cập trực tuyến: | https://link.springer.com/article/10.1007/s10231-022-01268-w https://dlib.phenikaa-uni.edu.vn/handle/PNK/7449 |
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oai:localhost:PNK-74492023-04-03T08:41:37Z Maximum relative distance between real rank-two and rank-one tensors Henrik, Eisenmann André, Uschmajew Frobenius norm rank-one approximation CC BY It is shown that the relative distance in Frobenius norm of a real symmetric order-d tensor of rank-two to its best rank-one approximation is upper bounded by 1−(1−1/d)d−1−−−−−−−−−−−−−√. This is achieved by determining the minimal possible ratio between spectral and Frobenius norm for symmetric tensors of border rank two, which equals (1−1/d)(d−1)/2. These bounds are also verified for arbitrary real rank-two tensors by reducing to the symmetric case. 2023-04-03T08:41:37Z 2023-04-03T08:41:37Z 2022 Book https://link.springer.com/article/10.1007/s10231-022-01268-w https://dlib.phenikaa-uni.edu.vn/handle/PNK/7449 en application/pdf Springer |
| institution |
Digital Phenikaa |
| collection |
Digital Phenikaa |
| language |
English |
| topic |
Frobenius norm rank-one approximation |
| spellingShingle |
Frobenius norm rank-one approximation Henrik, Eisenmann André, Uschmajew Maximum relative distance between real rank-two and rank-one tensors |
| description |
CC BY |
| format |
Book |
| author |
Henrik, Eisenmann André, Uschmajew |
| author_facet |
Henrik, Eisenmann André, Uschmajew |
| author_sort |
Henrik, Eisenmann |
| title |
Maximum relative distance between real rank-two and rank-one tensors |
| title_short |
Maximum relative distance between real rank-two and rank-one tensors |
| title_full |
Maximum relative distance between real rank-two and rank-one tensors |
| title_fullStr |
Maximum relative distance between real rank-two and rank-one tensors |
| title_full_unstemmed |
Maximum relative distance between real rank-two and rank-one tensors |
| title_sort |
maximum relative distance between real rank-two and rank-one tensors |
| publisher |
Springer |
| publishDate |
2023 |
| url |
https://link.springer.com/article/10.1007/s10231-022-01268-w https://dlib.phenikaa-uni.edu.vn/handle/PNK/7449 |
| _version_ |
1762184304840933376 |
| score |
8.891145 |