Name
Abstract | ||
|---|---|---|
This paper deals with the approximation of $$d$$ d -dimensional tensors, as discrete representations of arbitrary functions $$f(x_1,\ldots ,x_d)$$ f ( x 1 , , x d ) on $$[0,1]^d$$ [ 0 , 1 ] d , in the so-called tensor chain format. The main goal of this paper is to show that the construction of a tensor chain approximation is possible using skeleton/cross approximation type methods. The complete algorithm is described, computational issues are discussed in detail and the complexity of the algorithm is shown to be linear in $$d$$ d . Some numerical examples are given to validate the theoretical results. |
Year | DOI | Venue |
|---|---|---|
2012 | 10.1007/s00791-014-0218-7 | Computing and Visualization in Science |
Keywords | Field | DocType |
cross approximation,tensor chain format,41a63,skeleton decomposition,15a69,singular value decomposition,65f30 | Tensor density,Singular value decomposition,Mathematical optimization,Algebra,Tensor,Mathematical analysis,Mathematics | Journal |
Volume | Issue | ISSN |
15 | 6 | 1433-0369 |
Citations | PageRank | References |
7 | 0.49 | 14 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Mike Espig | 1 | 7 | 0.49 |
| Kishore Kumar Naraparaju | 2 | 9 | 1.20 |
| Jan Schneider | 3 | 7 | 0.49 |