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An alternative algorithm for a sliding window ULV decomposition. (English) Zbl 1089.65036

The authors present a modified ULV decomposition method, to approximate the singular value decomposition, for large scale low rank matrices that meets some specific requirements related to time varying applications in signal processing. The method diminishes storage requirements, its execution is \(O(n^2\)) and appends data on the top part of the matrix thus representing a viable alternative to existing methods. Computational examples illustrate the methods feasibility.

MSC:

65F30 Other matrix algorithms (MSC2010)
65F05 Direct numerical methods for linear systems and matrix inversion
65F50 Computational methods for sparse matrices
94A12 Signal theory (characterization, reconstruction, filtering, etc.)
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[1] Barlow, J. L., Yoon, P. A.: Solving recursive TLS problems using rank-revaling ULV decomposition. In: Proc. Workshop on TLS and Errors-in-variables (Van Huffel, S., ed.). Philadelphia, PA: SIAM Publications 1997, pp. 117–126. · Zbl 0892.62050
[4] Erbay, H., Barlow, J. L.: Recursive ULV decompositions and an alternative refinement algorithm. In: Adv. Sign. Proc. Alg., Arch. Impl. X (Luk, F. T., ed.). SPIE Proc. (Bellingham, WA) 2000, pp. 157–166.
[7] Fierro, R., Vanhamme, L., Van Huffel, S.: Total least squares algorithms based on rank-revealing complete orthogonal decompositions. Philadelphia, PA: SIAM Publications 1997, pp. 99–116. · Zbl 0928.62050
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