  This paper considers the problem of updating the rank-k truncated Singular
Value Decomposition (SVD) of matrices subject to the addition of new rows
and/or columns over time. Such matrix problems represent an important
computational kernel in applications such as Latent Semantic Indexing and
Recommender Systems. Nonetheless, the proposed framework is purely algebraic
and targets general updating problems. The algorithm presented in this paper
undertakes a projection view-point and focuses on building a pair of subspaces
which approximate the linear span of the sought singular vectors of the updated
matrix. We discuss and analyze two different choices to form the projection
subspaces. Results on matrices from real applications suggest that the proposed
algorithm can lead to higher accuracy, especially for the singular triplets
associated with the largest modulus singular values. Several practical details
and key differences with other approaches are also discussed.
