  This paper discusses a few algorithms for updating the approximate Singular
Value Decomposition (SVD) in the context of information retrieval by Latent
Semantic Indexing (LSI) methods. A unifying framework is considered which is
based on Rayleigh-Ritz projection methods. First, a Rayleigh-Ritz approach for
the SVD is discussed and it is then used to interpret the Zha--Simon algorithms
[SIAM J. Scient. Comput. vol. 21 (1999), pp. 782-791]. This viewpoint leads to
a few alternatives whose goal is to reduce computational cost and storage
requirement by projection techniques that utilize subspaces of much smaller
dimension. Numerical experiments show that the proposed algorithms yield
accuracies comparable to those obtained from standard ones at a much lower
computational cost.
