A note on tensor chain approximation

This paper deals with the approximation of $$d$$d-dimensional tensors, as discrete representations of arbitrary functions $$f(x_1,\ldots ,x_d)$$f(x1,…,xd) 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.

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