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Frontiers of Mathematics in China

, Volume 2, Issue 4, pp 501–526 | Cite as

Numerical multilinear algebra and its applications

  • Qi Liqun 
  • Sun Wenyu 
  • Wang Yiju 
Survey Article

Abstract

Numerical multilinear algebra (or called tensor computation), in which instead of matrices and vectors the higher-order tensors are considered in numerical viewpoint, is a new branch of computational mathematics. Although it is an extension of numerical linear algebra, it has many essential differences from numerical linear algebra and more difficulties than it. In this paper, we present a survey on the state of the art knowledge on this topic, which is incomplete, and indicate some new trends for further research. Our survey also contains a detailed bibliography as its important part. We hope that this new area will be receiving more attention of more scholars.

Keywords

Numerical multilinear algebra higher order tensor tensor decomposition lower rank approximation of tensor multi-way data analysis 

MSC

15A18 15A69 65F30 

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Copyright information

© Higher Education Press and Springer-Verlag 2007

Authors and Affiliations

  1. 1.Department of Applied MathematicsThe Hong Kong Polytechnic UniversityHong KongChina
  2. 2.School of Mathematics and Computer ScienceNanjing Normal UniversityNanjingChina
  3. 3.School of Operations Research and Management ScienceQufu Normal UniversityRizhaoChina

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