Quasioptimality of maximum-volume cross interpolation of tensors
| Autor: | Savostyanov, Dmitry V. |
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| Rok vydání: | 2013 |
| Předmět: | |
| Zdroj: | Linear Algebra and its Applications 458:217-244 (2014) |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1016/j.laa.2014.06.006 |
| Popis: | We consider a cross interpolation of high-dimensional arrays in the tensor train format. We prove that the maximum-volume choice of the interpolation sets provides the quasioptimal interpolation accuracy, that differs from the best possible accuracy by the factor which does not grow exponentially with dimension. For nested interpolation sets we prove the interpolation property and propose greedy cross interpolation algorithms. We justify the theoretical results and test the speed and accuracy of the proposed algorithm with convincing numerical experiments. Comment: Submitted to SIAM J Matr Anal Appl |
| Databáze: | arXiv |
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