TY - GEN
T1 - Fast adaptive interpolation of multi-dimensional arrays in tensor train format
AU - Savostyanov, Dmitry
AU - Oseledets, Ivan
PY - 2011/12/13
Y1 - 2011/12/13
N2 - Using recently proposed tensor train format for the representation of multi-dimensional dense arrays (tensors) we develop a fast interpolation method to approximate the given tensor by using only a small number of its elements. The algorithm is based on DMRG scheme, known among the quantum chemistry society. It is modified to make an interpolation on the adaptive set of tensor elements. The latter is selected using the maximum-volume principle which was previously used for the cross approximation schemes for matrices and 3-tensors. The numerical examples includes the interpolation of one- and many-dimensional functions on the uniform grids.
AB - Using recently proposed tensor train format for the representation of multi-dimensional dense arrays (tensors) we develop a fast interpolation method to approximate the given tensor by using only a small number of its elements. The algorithm is based on DMRG scheme, known among the quantum chemistry society. It is modified to make an interpolation on the adaptive set of tensor elements. The latter is selected using the maximum-volume principle which was previously used for the cross approximation schemes for matrices and 3-tensors. The numerical examples includes the interpolation of one- and many-dimensional functions on the uniform grids.
UR - http://www.scopus.com/inward/record.url?scp=83055196753&partnerID=8YFLogxK
U2 - 10.1109/nDS.2011.6076873
DO - 10.1109/nDS.2011.6076873
M3 - Conference contribution with ISSN or ISBN
AN - SCOPUS:83055196753
SN - 9781612848167
T3 - 2011 7th International Workshop on Multidimensional (nD) Systems, nDS 2011
BT - 2011 7th International Workshop on Multidimensional (nD) Systems, nDS 2011
T2 - 2011 7th International Workshop on Multidimensional (nD) Systems, nDS 2011
Y2 - 5 September 2011 through 7 September 2011
ER -