It applies also to block-terms approximations of tensors: for any $r$, a general tensor has a unique best $r$-block-terms approximations. Our result covers many other notions of tensor rank: symmetric rank, alternating rank, Chow rank, Segre-Veronese rank, Segre-Grassmann rank, Segre-Chow rank, Veronese-Grassmann rank, Veronese-Chow rank, Segre-Veronese-Grassmann rank, Segre-Veronese-Chow rank, and more - in all cases, a unique best rank-$r$ approximation almost always exist. Over $\mathbb$, any tensor almost always has a unique best rank-$r$ approximation when $r$ is less than the generic rank. Low-rank tensor approximations are plagued by a well-known problem - a tensor may fail to have a best rank-$r$ approximation.
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |