Block gram-schmidt downdating

Given positive integers m, n, and p, where m ≥ n+p and p ∗ n. A method is proposed to modify the QR decomposition of X ∈ ℝ^{m × n} to produce a QR decomposition of X with p rows deleted. The algorithm is based upon the classical block Gram-Schmidt method, requires an approximation of the norm of the inverse of a triangular matrix, has O(mnp) operations, and achieves an accuracy in the matrix 2-norm that is comparable to similar bounds for related procedures for p = 1 in the vector 2-norm. Since the algorithm is based upon matrixmatrix operations, it is appropriate for modern cache oriented computer architectures.