The Average Condition Number of Most Tensor Rank Decomposition Problems is Infinite
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Springer
2023
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oai:localhost:PNK-74462023-04-03T08:10:18Z The Average Condition Number of Most Tensor Rank Decomposition Problems is Infinite Carlos, Beltrán Paul, Breiding Nick, Vannieuwenhoven sum of rank-1 tensors structured perturbations CC BY The tensor rank decomposition, or canonical polyadic decomposition, is the decomposition of a tensor into a sum of rank-1 tensors. The condition number of the tensor rank decomposition measures the sensitivity of the rank-1 summands with respect to structured perturbations. Those are perturbations preserving the rank of the tensor that is decomposed. On the other hand, the angular condition number measures the perturbations of the rank-1 summands up to scaling. We show for random rank-2 tensors that the expected value of the condition number is infinite for a wide range of choices of the density. 2023-04-03T08:10:18Z 2023-04-03T08:10:18Z 2022 Book https://dlib.phenikaa-uni.edu.vn/handle/PNK/7446 en application/pdf Springer |
| institution |
Digital Phenikaa |
| collection |
Digital Phenikaa |
| language |
English |
| topic |
sum of rank-1 tensors structured perturbations |
| spellingShingle |
sum of rank-1 tensors structured perturbations Carlos, Beltrán Paul, Breiding Nick, Vannieuwenhoven The Average Condition Number of Most Tensor Rank Decomposition Problems is Infinite |
| description |
CC BY |
| format |
Book |
| author |
Carlos, Beltrán Paul, Breiding Nick, Vannieuwenhoven |
| author_facet |
Carlos, Beltrán Paul, Breiding Nick, Vannieuwenhoven |
| author_sort |
Carlos, Beltrán |
| title |
The Average Condition Number of Most Tensor Rank Decomposition Problems is Infinite |
| title_short |
The Average Condition Number of Most Tensor Rank Decomposition Problems is Infinite |
| title_full |
The Average Condition Number of Most Tensor Rank Decomposition Problems is Infinite |
| title_fullStr |
The Average Condition Number of Most Tensor Rank Decomposition Problems is Infinite |
| title_full_unstemmed |
The Average Condition Number of Most Tensor Rank Decomposition Problems is Infinite |
| title_sort |
average condition number of most tensor rank decomposition problems is infinite |
| publisher |
Springer |
| publishDate |
2023 |
| url |
https://dlib.phenikaa-uni.edu.vn/handle/PNK/7446 |
| _version_ |
1762184304565157888 |
| score |
8.891145 |