期刊
SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS
卷 31, 期 2, 页码 248-271出版社
SIAM PUBLICATIONS
DOI: 10.1137/070688316
关键词
tensor; multilinear; rank; approximation; Grassmann manifold; Newton
We derive a Newton method for computing the best rank-(r(1), r(2), r(3)) approximation of a given J x K x L tensor A. The problem is formulated as an approximation problem on a product of Grassmann manifolds. Incorporating the manifold structure into Newton's method ensures that all iterates generated by the algorithm are points on the Grassmann manifolds. We also introduce a consistent notation for matricizing a tensor, for contracted tensor products and some tensor-algebraic manipulations, which simplify the derivation of the Newton equations and enable straightforward algorithmic implementation. Experiments show a quadratic convergence rate for the Newton-Grassmann algorithm.
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