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Numerical Algorithms manuscript No. (will be inserted by the editor)

Summary: Numerical Algorithms manuscript No.
(will be inserted by the editor)
Differential-geometric Newton method for the best
rank-(R1, R2, R3) approximation of tensors
Mariya Ishteva Lieven De Lathauwer
P.-A. Absil Sabine Van Huffel
Received: date / Accepted: date
Abstract 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-(R1, R2, R3) 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 [15]. This kind of
algorithms are useful for many problems.
Keywords multilinear algebra · higher-order tensor · higher-order singular value
decomposition · rank-(R1, R2, R3) reduction · quotient manifold · differential-geometric
optimization · Newton's method · Tucker compression
This paper presents research results of the Belgian Network DYSCO (Dynamical Systems,
Control, and Optimization), funded by the Interuniversity Attraction Poles Programme, initi-
ated by the Belgian State, Science Policy Office. The scientific responsibility rests with its


Source: Absil, Pierre-Antoine - Département d'ingénierie Mathématique, Université Catholique de Louvain


Collections: Mathematics