<tt> <scp>pyaneti</scp> </tt> – II. A multidimensional Gaussian process approach to analysing spectroscopic time-series

TT-cross approximation for multidimensional arrays

Article history: Received 19 July 2009 Accepted 27 July 2009 Available online 21 August 2009 Submitted by V. Sergeichuk AMS classification: 15A12 65F10 65F15

Tangent Cones to TT Varieties

As already done for the matrix case in [6, p.256], [1, Thm. 6.1, p.1872] and [10, Thm. 3.2] we give a parametrization of the Bouligand tangent cone of the variety of tensors of bounded TT rank. We discuss how the proof generalizes to any binary hierarchical format. The parametrization can be rewritten as an orthogonal sum of TT tensors. Its retraction onto the variety is particularly easy to co...

A method of time-time analysis: The TT-transform

A novel technique of analysis of an arbitrary primary time series into a set of secondary, timelimited, local, constituent time series, the TT-transform, is presented. The time–time representation is derived from the S-transform, a method of representation of a real time series as a set of complex, time-localized spectra. When integrated over time, the S-transform becomes the Fourier transform ...

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DMRG Approach to Fast Linear Algebra in the TT-Format

In this paper the concept of DMRG minimization scheme is extended for important operations in the TT-format, like matrix-by-vector product and conversion from the canonical format to the TT-format. Fast algorithms are implemented in the TT-Toolbox stabilization scheme based on randomization is proposed, and the comparison with the direct method is performed on a sequence of matrices and vectors...