Two ultrawideband Gaussian beam summation (UWB-GBS) algorithms are presented and then explored in the context of calculating UWB focusing by curved interfaces. The favorable features of the basic algorithm are: (1) The same lattice of beams is used for all frequencies, and (2) it utilizes isodiffracting Gaussian beams with frequency-independent propagation parameters, which also yield stable and localized expansion coefficients for all frequencies. We then present a modified multiband algorithm that is more efficient if the signal bandwidth is larger than one octave. Here the signal bandwidth is divided into a self-consistent hierarchy of one-octave subbands such that the beam sets at the lower-frequency bands are decimated subsets of those at the highest band, so that only the set of GBs at the highest band needs to be traced, while for the lower bands one may use properly decimated subsets. The numerical example demonstrates the effectiveness, the localization, and the uniformity of the UWB-GBS representation in the focal zone. Concluding remarks contain comparisons between the proposed method and Kirchhoff aperture-based alternatives.