  The Laser Interferometer Space Antenna (LISA) is a planned space-based
gravitational wave telescope with the goal of measuring gravitational waves in
the milli-Hertz frequency band, which is dominated by millions of Galactic
binaries. While some of these binaries produce signals that are loud enough to
stand out and be extracted, most of them blur into a confusion foreground.
Current methods for analyzing the full frequency band recorded by LISA to
extract as many Galactic binaries as possible and to obtain Bayesian posterior
distributions for each of the signals are computationally expensive. We
introduce a new approach to accelerate the extraction of the best fitting
solutions for Galactic binaries across the entire frequency band from data with
multiple overlapping signals. Furthermore, we use these best fitting solutions
to omit the burn-in stage of a Markov chain Monte Carlo method and to take full
advantage of GPU-accelerated signal simulation, allowing us to compute
posterior distributions in 2 seconds per signal on a laptop-grade GPU.
