# Template Bank for Compact Binary Coalescence Searches in Gravitational Wave Data: A General Geometric Placement Algorithm

## TL;DR

This paper presents a new geometric algorithm for efficiently placing template waveforms in gravitational wave data analysis, improving search accuracy for various compact binary mergers.

## Contribution

The paper introduces a general, computationally efficient template placement algorithm based on phase space linearization and singular value decomposition, applicable to any waveform model.

## Key findings

- Constructed template banks for multiple binary merger types.
- Demonstrated the algorithm's efficiency and broad applicability.
- Improved search sensitivity for gravitational wave detectors.

## Abstract

We introduce an algorithm for placing template waveforms for the search of compact binary mergers in gravitational wave interferometer data. We exploit the smooth dependence of the amplitude and unwrapped phase of the frequency-domain waveform on the parameters of the binary. We group waveforms with similar amplitude profiles and perform a singular value decomposition of the phase profiles to obtain an orthonormal basis for the phase functions. The leading basis functions span a lower-dimensional linear space in which the unwrapped phase of any physical waveform is well approximated. The optimal template placement is given by a regular grid in the space of linear coefficients. The algorithm is applicable to any frequency-domain waveform model and detector sensitivity curve. It is computationally efficient and requires little tuning. Applying this method, we construct a set of template banks suitable for the search of aligned-spin binary neutron star, neutron-star--black-hole and binary black hole mergers in LIGO--Virgo data.