publication . Article . Other literature type . Preprint . 2011

A Nonlinear GMRES Optimization Algorithm for Canonical Tensor Decomposition

Hans De Sterck;
Open Access
  • Published: 26 May 2011 Journal: SIAM Journal on Scientific Computing, volume 34, pages A1351-A1379 (issn: 1064-8275, eissn: 1095-7197, Copyright policy)
  • Publisher: Society for Industrial & Applied Mathematics (SIAM)
A new algorithm is presented for computing a canonical rank-R tensor approximation that has minimal distance to a given tensor in the Frobenius norm, where the canonical rank-R tensor consists of the sum of R rank-one components. Each iteration of the method consists of three steps. In the first step, a tentative new iterate is generated by a stand-alone one-step process, for which we use alternating least squares (ALS). In the second step, an accelerated iterate is generated by a nonlinear generalized minimal residual (GMRES) approach, recombining previous iterates in an optimal way, and essentially using the stand-alone one-step process as a preconditioner. In...
Persistent Identifiers
arXiv: Computer Science::Numerical Analysis
free text keywords: Applied Mathematics, Computational Mathematics, Mathematics - Numerical Analysis, Computer Science - Numerical Analysis, Nonlinear system, Tensor, Matrix norm, Nonlinear programming, Preconditioner, Line search, Generalized minimal residual method, Mathematics, Iterated function
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