651 research outputs found
On best rank one approximation of tensors
In this paper we suggest a new algorithm for the computation of a best rank
one approximation of tensors, called alternating singular value decomposition.
This method is based on the computation of maximal singular values and the
corresponding singular vectors of matrices. We also introduce a modification
for this method and the alternating least squares method, which ensures that
alternating iterations will always converge to a semi-maximal point. (A
critical point in several vector variables is semi-maximal if it is maximal
with respect to each vector variable, while other vector variables are kept
fixed.) We present several numerical examples that illustrate the computational
performance of the new method in comparison to the alternating least square
method.Comment: 17 pages and 6 figure
Fast truncation of mode ranks for bilinear tensor operations
We propose a fast algorithm for mode rank truncation of the result of a
bilinear operation on 3-tensors given in the Tucker or canonical form. If the
arguments and the result have mode sizes n and mode ranks r, the computation
costs . The algorithm is based on the cross approximation of
Gram matrices, and the accuracy of the resulted Tucker approximation is limited
by square root of machine precision.Comment: 9 pages, 2 tables. Submitted to Numerical Linear Algebra and
Applications, special edition for ICSMT conference, Hong Kong, January 201
- …