  We introduce a reduced basis approach as a new paradigm for modeling,
representing and searching for gravitational waves. We construct waveform
catalogs for non-spinning compact binary coalescences, and we find that for
accuracies of 99% and 99.999% the method generates a factor of about $10-10^5$
fewer templates than standard placement methods. The continuum of gravitational
waves can be represented by a finite and comparatively compact basis. The
method is robust under variations in the noise of detectors, implying that only
a single catalog needs to be generated.
