A modified Newton's method for best rank-one approximation to tensors

DOI10.1016/j.amc.2009.12.019zbMath1226.65031OpenAlexW2072422975MaRDI QIDQ979270

Yannan Chen, Jingya Chang, Wen-Yu Sun

Publication date: 25 June 2010

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.amc.2009.12.019

zbMATH Keywords

global convergencenumerical experimentsalternating least squares algorithmmodified Newton's methodtensor computationGRQ-Newton methodJacobi-Gauss-Newton algorithmprojective directionrank-one approximation

Mathematics Subject Classification ID

Numerical solutions to overdetermined systems, pseudoinverses (65F20) Numerical mathematical programming methods (65K05) Methods of quasi-Newton type (90C53) Vector and tensor algebra, theory of invariants (15A72)

Related Items

Algorithms for structure preserving best rank-one approximations of partially symmetric tensors, Successive unconstrained dual optimization method for~rank-one approximation to tensors, A locally convergent Jacobi iteration for the tensor singular value problem

Cites Work

• Eigenvalues and invariants of tensors
• Some additional results on principal components analysis of three-mode data by means of alternating least squares algorithms
• Principal component analysis of three-mode data by means of alternating least squares algorithms
• Eigenvalues of a real supersymmetric tensor
• Rank and eigenvalues of a supersymmetric tensor, the multivariate homogeneous polynomial and the algebraic hypersurface it defines
• Numerical multilinear algebra and its applications
• Optimization theory and methods. Nonlinear programming
• Analysis of individual differences in multidimensional scaling via an \(n\)-way generalization of ``Eckart-Young decomposition
• An alternating least squares algorithm for PARAFAC2 and three-way DEDICOM
• Rank-One Approximation to High Order Tensors
• A Multilinear Singular Value Decomposition
• On the Best Rank-1 and Rank-(R₁ ,R₂ ,. . .,R_N) Approximation of Higher-Order Tensors
• Jacobi Angles for Simultaneous Diagonalization