Modified Gram-Schmidt-based downdating technique for ULV decompositions with applications to recursive TLS problems

Details Modified Gram-Schmidt-based downdating technique for ULV decompositions with applications to recursive TLS problems Modified Gram-Schmidt-based downdating technique for ULV decompositions with applications to recursive TLS problems

Nov 1999

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1999spie.3807..247b&link_type=abstract

Proc. SPIE Vol. 3807, p. 247-257, Advanced Signal Processing Algorithms, Architectures, and Implementations IX, Franklin T. Luk;

Statistics

Computation

Scientific paper

The ULV decomposition (ULVD) is an important member of a class of rank-revealing two-sided orthogonal decompositions used to approximate the singular value decomposition (SVD). The ULVD can be updated and downdated much faster than the SVD, hence its utility in the solution of recursive total least squares (TLS) problems. However, the robust implementation of ULVD after the addition and deletion of rows (called updating and downdating respectively) is not altogether straightforward. When updating or downdating the ULVD, the accurate computation of the subspaces necessary to solve the TLS problem is of great importance. In this paper, algorithms are given to compute simple parameters that can often show when good subspaces have been computed.

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