  Low-latency gravitational wave search pipelines such as GstLAL 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 huge template 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, applicable
for large template banks. This follow-up paper demonstrates the application of
a block-wise randomized matrix factorization (RMF) algorithm for computing
low-rank factorizations at a preset average fractional loss of SNR. This new
scheme is shown to be more efficient in the context of the LLOID framework of
the GstLAL search pipeline. Further, it is well-known that for huge template
banks, the total computational cost of the search is dominated by
reconstructing the detection statistic compared to that of filtering the data.
However, optimizing the reconstruction cost has not been addressed
satisfactorily so far in the available literature. We show that it is possible
to approximately reconstruct the time-series of the matched-filter detection
statistic at a fraction of the total cost using the matching pursuit algorithm.
Combining the two algorithms presented in this paper can handle online searches
involving large template banks more efficiently. We have analyzed the total
computational cost in detail and offer various tips for optimally applying the
RMF scheme in different parts of the parameter space. The algorithms presented
in this paper are designed in a suitable manner that can be efficiently
implemented over a distributed computing architecture.
