Numerical multilinear algebra and its applications

被引：14

作者：

Qi L. ^{[1
]}

Sun W. ^{[2
]}

Wang Y. ^{[1
,3
]}

机构：

[1] Department of Applied Mathematics, Hong Kong Polytechnic University, Hong Kong

[2] School of Mathematics and Computer Science, Nanjing Normal University

[3] School of Operations Research and Management Science, Qufu Normal University

来源：

Frontiers of Mathematics in China | 2007年 / 2卷 / 4期

基金：

中国国家自然科学基金; 高等学校博士学科点专项科研基金;

关键词：

Higher order tensor; Lower rank approximation of tensor; Multi-way data analysis; Numerical multilinear algebra; Tensor decomposition;

D O I：

10.1007/s11464-007-0031-4

中图分类号：

学科分类号：

摘要：

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. © 2007 Higher Education Press and Springer-Verlag.

引用

页码：501 / 526

页数：25

共 83 条

[1]

Alon N., De La Vega W.F., Kannan R., Et al., Random sampling and approximation of max-csps, J Comput System Sci, 67, pp. 212-243, (2003)

[2]

Bergman G.M., Ranks of tensors and change of base field, J Algebra, 11, pp. 613-621, (1969)

[3]

Bienvenu G., Kopp L., Optimality of high-resolution array processing using the eigen-system approach, IEEE Trans ASSP, 31, pp. 1235-1248, (1983)

[4]

Cao X.R., Liu R.W., General approach to blind source separation, IEEE Trans Signal Processing, 44, pp. 562-570, (1996)

[5]

Cardoso J.F., Super-symmetric decomposition of the forth-order cumulant tensor. Blind identification of more sources than sensors, Proceedings of the IEEE International Conference on Acoust, Speech, and Signal Processing (ICASSP'91), (1991)

[6]

Cardoso J.F., High-order contrasts for independent component analysis, Neural Computation, 11, pp. 157-192, (1999)

[7]

Caroll J.D., Chang J.J., Analysis of individual differences in multidimensional scaling via n-way generalization of Eckart-Young decomposition, Psychometrika, 35, pp. 283-319, (1970)

[8]

Comon P., Tensor diagonalization, a useful tool in signal processing, 10th IFAC Symposium on System Identification, 1, pp. 77-82, (1994)

[9]

Comon P., Independent component analysis, a new concept?, Signal Processing, Special Issue on Higher-Order Statistics, 36, pp. 287-314, (1994)

[10]

Comon P., Mourrain B., Decomposition of quantics in sums of powers of linear forms, Signal Processing, Special Issue on Higher-Order Statistics, 53, pp. 96-107, (1996)

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