A Cholesky QR type algorithm for computing tall-skinny QR factorization with column pivoting

We consider computing the QR factorization with column pivoting (QRCP) for a tall and skinny matrix, which has important applications including low-rank approximation and rank determination. Motivated by recent progresses of Cholesky QR type algorithms for tall-skinny QR factorization (without pivoting), we propose a new Cholesky QR type algorithm for tall-skinny QRCP, which we call Iterative Cholesky QR with Column Pivoting (Ite-CholQR-CP). Through performance evaluation, it is confirmed that Ite-CholQR-CP provides a solution as accurate as that by Householder QR with column pivoting (HQR-CP), which is a widely-used conventional algorithm. In addition, Ite-CholQR-CP outperforms HQR-CP in execution time in single node and distributed parallel computations: up to 45x (single node computation) and 27x (distributed parallel computation) speedup.