TY - JOUR

T1 - Block gram-schmidt downdating

AU - Barlow, Jesse L.

N1 - Publisher Copyright:
Copyright © 2015, Kent State University.

PY - 2014

Y1 - 2014

N2 - 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 ∈ ℝm × 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.

AB - 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 ∈ ℝm × 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.

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M3 - Article

AN - SCOPUS:84928879960

VL - 43

SP - 163

EP - 187

JO - Electronic Transactions on Numerical Analysis

JF - Electronic Transactions on Numerical Analysis

SN - 1068-9613

ER -