  In our earlier work [Fareed et al., Comput. Math. Appl. 75 (2018), no. 6,
1942-1960], we proposed an incremental SVD algorithm with respect to a weighted
inner product to compute the proper orthogonal decomposition (POD) of a set of
simulation data for a partial differential equation (PDE) without storing the
data. In this work, we perform an error analysis of the incremental SVD
algorithm. We also modify the algorithm to incrementally update both the SVD
and an error bound when a new column of data is added. We show the algorithm
produces the exact SVD of an approximate data matrix, and the operator norm
error between the approximate and exact data matrices is bounded above by the
computed error bound. This error bound also allows us to bound the error in the
incrementally computed singular values and singular vectors. We illustrate our
analysis with numerical results for three simulation data sets from a 1D
FitzHugh-Nagumo PDE system with various choices of the algorithm truncation
tolerances.
