  Low-latency gravitational wave search pipelines such as LLOID take advantage
of low-rank factorization of the template matrix via singular value
decomposition (SVD). With unprecedented improvements in detector bandwidth and
sensitivity in advanced-LIGO and Virgo detectors, one expects several orders of
magnitude increase in the size of template banks. This poses a formidable
computational challenge in factorizing extremely large matrices. Previously,
[in Kulkarni et al. [6]], we introduced the idea of random projection
(RP)-based matrix factorization as a computationally viable alternative to SVD,
for such large template banks. In this follow-up paper, we demonstrate the
application of a block-wise randomized matrix factorization (RMF) scheme using
which one can compute the desired low-rank factorization corresponding to a
fixed average SNR loss (h{\delta}\r{ho}/\r{ho}i). Unlike the SVD approach, this
new scheme affords a much more efficient way of matrix factorization especially
in the context of LLOID search pipelines. It is a well-known fact that for very
large template banks, the total computational cost is dominated by the cost of
reconstruction of the detection statistic and that the cost of filtering the
data is insignificant in comparison. We are unaware of any previous work in
literature that has tried to squarely address this issue of optimizing the
reconstruction cost. We provide a possible solution to reduce the
reconstruction cost using the matching pursuit(MP) algorithm. We show that it
is possible to approximately reconstruct the time-series of the detection
statistic at a fraction of the total cost using our MP algorithm. The
combination of RMF along with MP can handle large template banks more
efficiently in comparison to the direct application of SVD. Results from
several numerical simulations have been presented to demonstrate their
efficacy.
