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Low-latency gravitational wave search pipelines such as GstLAL take advantageof low-rank factorization of the template matrix via singular valuedecomposition (SVD). With unprecedented improvements in detector bandwidth andsensitivity in advanced-LIGO and Virgo detectors, one expects several orders ofmagnitude increase in the size of template banks. This poses a formidablecomputational challenge in factorizing huge template matrices. Previously, [inKulkarni et al. [6]], we introduced the idea of random projection (RP)-basedmatrix factorization as a computationally viable alternative to SVD, applicablefor large template banks. This follow-up paper demonstrates the application ofa block-wise randomized matrix factorization (RMF) algorithm for computinglow-rank factorizations at a preset average fractional loss of SNR. This newscheme is shown to be more efficient in the context of the LLOID framework ofthe GstLAL search pipeline. Further, it is well-known that for huge templatebanks, the total computational cost of the search is dominated byreconstructing the detection statistic compared to that of filtering the data.However, optimizing the reconstruction cost has not been addressedsatisfactorily so far in the available literature. We show that it is possibleto approximately reconstruct the time-series of the matched-filter detectionstatistic at a fraction of the total cost using the matching pursuit algorithm.Combining the two algorithms presented in this paper can handle online searchesinvolving large template banks more efficiently. We have analyzed the totalcomputational cost in detail and offer various tips for optimally applying theRMF scheme in different parts of the parameter space. The algorithms presentedin this paper are designed in a suitable manner that can be efficientlyimplemented over a distributed computing architecture.

Random projections in gravitational-wave searches from compact binaries II: efficient reconstruction of the detection statistic