Frontiers of Mathematics in China >

2007 , Vol. 2 >Issue 4: 501 - 526

DOI: https://doi.org/10.1007/s11464-007-0031-4

Numerical multilinear algebra and its applications

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  • 1.Department of Applied Mathematics, The Hong Kong Polytechnic University, Hong Kong, China; 2.School of Mathematics and Computer Science, Nanjing Normal University, Nanjing 210097, China; 3.Department of Applied Mathematics, The Hong Kong Polytechnic University, Hong Kong, China; School of Operations Research and Management Science, Qufu Normal University, Rizhao 276800, China;

Published date: 05 Dec 2007

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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 diffculties 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.

Cite this article

QI Liqun, SUN Wenyu, WANG Yiju . Numerical multilinear algebra and its applications[J]. Frontiers of Mathematics in China, 2007 , 2(4) : 501 -526 . DOI: 10.1007/s11464-007-0031-4

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