Journal
NUMERICAL ALGORITHMS
Volume 51, Issue 2, Pages 179-194Publisher
SPRINGER
DOI: 10.1007/s11075-008-9251-2
Keywords
Multilinear algebra; Higher-order tensor; Higher-order singular value decomposition; Rank-(R-1, R-2, R-3) reduction; Quotient manifold; Differential-geometric optimization; Newton's method; Tucker compression
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An increasing number of applications are based on the manipulation of higher-order tensors. In this paper, we derive a differential-geometric Newton method for computing the best rank-(R (1), R (2), R (3)) approximation of a third-order tensor. The generalization to tensors of order higher than three is straightforward. We illustrate the fast quadratic convergence of the algorithm in a neighborhood of the solution and compare it with the known higher-order orthogonal iteration (De Lathauwer et al., SIAM J Matrix Anal Appl 21(4):1324-1342, 2000). This kind of algorithms are useful for many problems.
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