Implementing QR factorization updating algorithms on GPUs

Linear least squares problems are commonly solved by QR factorization. When multiple solutions have to be computed with only minor changes in the underlying data, knowledge of the difference between the old data set and the new one can be used to update an existing factorization at reduced computational cost. This paper investigates the viability of implementing QR updating algorithms on GPUs. We demonstrate that GPU-based updating for removing columns achieves speed-ups of up to 13.5x compared with full GPU QR factorization. Other updates achieve speed-ups under certain conditions, and we characterize what these conditions are.