Block Gram-Schmidt downdating

Given positive integers m, n, and p, where m [greater than or equal to] n + p and p ≪ n. A method is proposed to modify the QR decomposition of X ∈ [R.sup.mxn] 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 matrix-matrix operations, it is appropriate for modern cache oriented computer architectures. Key words. QR decomposition, singular value decomposition, orthogonality, downdating, matrix-matrix operations.