Implementing QR factorization updating algorithms on GPUs

Linear least squares problems are commonly solved by QR factorization. When multiple solutions need to be computed with only minor changes in the underlying data, knowledge of the difference between the old data set and the new can be used to update an existing factorization at reduced computational cost. We investigate the viability of implementing QR updating algorithms on GPUs and demonstrate that GPU-based updating for removing columns achieves speed-ups of up to 13.5× compared with full GPU QR factorization. We characterize the conditions under which other types of updates also achieve speed-ups.