Fast adaptive interpolation of multi-dimensional arrays in tensor train format

By Dmitry V. Savostyanov, Ivan V. Oseledets. 2011

160 citations recorded by the source corpus.

Subfields: Computational Mathematics, Computational Mechanics, Computational Theory and Mathematics

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Mathematics

1. Sergey V. Dolgov
2. Dmitry V. Savostyanov
3. Boris N. Khoromskij
4. Christine Tobler
5. Ivan V. Oseledets
6. Roman Andreev
7. V. Dolgov
8. Vladimir A. Kazeev

In Computational Mechanics

1. Christine Tobler
2. Sergey V. Dolgov
3. Dmitry V. Savostyanov
4. Boris N. Khoromskij
5. Ivan V. Oseledets
6. Roman Andreev
7. Sertac Karaman
8. Youssef M. Marzouk

In Computational Theory and Mathematics

1. Christine Tobler
2. Dmitry V. Savostyanov
3. Sergey V. Dolgov
4. Boris N. Khoromskij
5. Ivan V. Oseledets
6. Roman Andreev
7. V. Dolgov
8. Vladimir A. Kazeev

Citations in the corpus

• A literature survey of low‐rank tensor approximation techniques (2013, neutral): “A cross approximation method for the TT decomposition has been proposed in [214,231].”
• Multilevel preconditioning and low‐rank tensor iteration for space–time simultaneous discretizations of parabolic PDEs (2015, methodology): “As an alternative to full pointwise inversion of g with subsequent truncation, we investigate the approximation of the tensor h by means of black box approximation [43, 44, 45, 46, 47].”
• Efficient High-Dimensional Stochastic Optimal Motion Control using Tensor-Train Decomposition (2015, background): “Rank-adaptive versions of this algorithm exist and can be found in [23].”
• Fast Solution of Parabolic Problems in the Tensor Train/Quantized Tensor Train Format with Initial Application to the Fokker-Planck Equation (2012, methodology): “On the other hand, the advantages of the QTT-format motivate us to treat the problem from a new point of view: we consider the time as an independent dimension and introduce a discretization of the whole differential equation with all spatial and time dimension connected in one large linear system.”
• Alternating Minimal Energy Methods for Linear Systems in Higher Dimensions (2013, unknown): “The DMRG was adopted for novel tensor formats (see references above) and new problems, including adaptive high–dimensional interpolation [37] and solution of linear systems [9, 18].”
• Superfast Fourier Transform Using QTT Approximation (2012, methodology): “The complexity of QTT-FFT is O (R 3 log 2 n) and TT-ACA algorithm [49] requires O (R 3 log n) operations for each iteration/ sweep .”