Computing the signal subspaces of a sparse and/or structured matrix

Ricardo D. Fierro

doi:10.1117/12.279498

24 October 1997 Computing the signal subspaces of a sparse and/or structured matrix

Ricardo D. Fierro

Proceedings Volume 3162, Advanced Signal Processing: Algorithms, Architectures, and Implementations VII; (1997) https://doi.org/10.1117/12.279498
Event: Optical Science, Engineering and Instrumentation '97, 1997, San Diego, CA, United States

Abstract

Many techniques involve the computation of singular subspaces associated with an extreme cluster of singular values of an m X n data matrix A. Frequently A is sparse and/or structured, which usually means matrix-vector multiplications involving A and its transpose can be done with much less than (sigma) (mn) flops, and A and its transpose can be stored in static data structures with much less than (sigma) )(mn) storage locations. Standard complete orthogonal decompositions may be unattractive due to the computational and dynamic storage overhead associated with the initial preprocessing of the data. We describe an efficient Matlab implementation of the low-rank ULV algorithm for extracting reliable and accurate approximations to the singular subspaces associated with the cluster of large singular values without altering the matrix. The user can choose any principal singular vector estimator to underwrite the algorithm, may call a specialized routine to compute matrix-vector products involving A and its transpose, and can choose the desired level of accuracy of a residual. The main computational savings stems from preserving A and avoiding the explicit formation of unwanted information.

Citation Download Citation

Ricardo D. Fierro "Computing the signal subspaces of a sparse and/or structured matrix", Proc. SPIE 3162, Advanced Signal Processing: Algorithms, Architectures, and Implementations VII, (24 October 1997); https://doi.org/10.1117/12.279498

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