Orthogonal tensor decompositions

Kolda, Tamara G.

Sandia National Laboratories

关键词: Orthogonal Transformations;    Tensors;    Matrices;    Mathematics;    99 General And Miscellaneous//Mathematics, Computing, And Information Science;   

DOI  :  10.2172/755101
RP-ID  :  SAND2000-8566
RP-ID  :  AC04-94AL85000
RP-ID  :  755101

美国|英语

来源: UNT Digital Library

【 摘 要 】

The authors explore the orthogonal decomposition of tensors (also known as multi-dimensional arrays or n-way arrays) using two different definitions of orthogonality. They present numerous examples to illustrate the difficulties in understanding such decompositions. They conclude with a counterexample to a tensor extension of the Eckart-Young SVD approximation theorem by Leibovici and Sabatier [Linear Algebra Appl. 269(1998):307--329].