Extended Lanczos Bidiagonalization Algorithm for Low Rank Approximation and its Applications

Wang, Xuansheng;Glineur, François;Lu, Linzhang;Van Dooren, Paul
(2016) Journal of Computational and Applied Mathematics — n° 301, p. 213-229 (2016)

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Authors
  • Wang, XuanshengShenzhen Institute of Information Technology, China
    Author
  • Glineur, Françoisorcid-logoUCLouvain
    Author
  • Lu, LinzhangGuizhou Normal University, P.R. China
    Author
  • Van Dooren, PaulUCLouvain
    Author
Abstract
(en) We propose an extended Lanczos bidiagonalization algorithm for finding a low rank approximation of a given matrix. We show that this method can yield better low-rank approximations than standard Lanczos bidiagonalization algorithm, without increasing the cost too much. We also describe a partial reorthogonalization process that can be used to maintain an adequate level of orthogonality of the Lanczos vectors in order to produce accurate low-rank approximations. We demonstrate the effectiveness and applicability of our algorithm for a number of applications.
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Wang, X., Glineur, F., Lu, L., & Van Dooren, P. (2016). Extended Lanczos Bidiagonalization Algorithm for Low Rank Approximation and its Applications. Journal of Computational and Applied Mathematics, 301, 213-229. https://doi.org/10.1016/j.cam.2015.12.039 (Original work published 2016)