|Appears in Collections:||Computing Science and Mathematics Journal Articles|
|Peer Review Status:||Refereed|
|Title:||On tensor decomposition, sparse interpolation and Padé approximation|
|Keywords:||tensor decomposition, sparse interpolation, Gaussian integration,|
Padé approximation, exponential analysis
MSC: Primary 41A55
Secondary 41A25, 42B35 †
|Citation:||Cuyt A, Lee W & Yang X (2016) On tensor decomposition, sparse interpolation and Padé approximation. Jaen Journal on Approximation, 8 (1), pp. 33-58. http://www.ujaen.es/revista/jja/pdf/pre/jja-0008-01-16-3.pdf.|
|Abstract:||What is the connection of tensor decomposition in multilinear algebra with exponential analysis from signal processing, sparse interpolation from computer algebra, Gaussian quadrature from numerical analysis, and Padé approximation theory? These seemingly unrelated and diverse topics are nevertheless deeply intertwined, as we explain here. However, several of these connections have remained unexplored. The various reformulations bring forth new ways to approach the problem of tensor decomposition (see Section 7) and suggestions for generalizations of existing methods (see Section 6). This may lead to important results since tensor decomposition has a number of grand applications , among others in chemometrics, neuroscience, computer vision, social network analysis, big data and the like. In Section 1 we introduce the problem statement. Subsequently the connections are first established for two-dimensional tensors in the sections 2 and 3. Higher dimensional tensors are dealt with in the sections 4 and 5, with a discussion of the connections to the mentioned topics in the sections 6 and 7. We conclude in Section 8 with an illustration of the interrelationships and of our novel approach. Both the existing method presented in Section 5 and the new technique presented in Section 7 are shown.|
|Rights:||The publisher does not allow this work to be made publicly available in this Repository. Please use the Request a Copy feature at the foot of the Repository record to request a copy directly from the author. You can only request a copy if you wish to use this work for your own research or private study.|
|jja-0008-01-16-3.pdf||Fulltext - Published Version||215.28 kB||Adobe PDF||Under Permanent Embargo Request a copy|
Note: If any of the files in this item are currently embargoed, you can request a copy directly from the author by clicking the padlock icon above. However, this facility is dependent on the depositor still being contactable at their original email address.
This item is protected by original copyright
Items in the Repository are protected by copyright, with all rights reserved, unless otherwise indicated.
If you believe that any material held in STORRE infringes copyright, please contact firstname.lastname@example.org providing details and we will remove the Work from public display in STORRE and investigate your claim.