A new algorithm for downdating a QR decomposition is presented. We show that, when the columns in the Q factor from the Modified gram-schmidt QR decomposition of a matrix X are exactly orthonormal, the gram-schmidt do...
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A new algorithm for downdating a QR decomposition is presented. We show that, when the columns in the Q factor from the Modified gram-schmidt QR decomposition of a matrix X are exactly orthonormal, the gram-schmidt downdating algorithm for the QR decomposition of X is equivalent to downdating the full Householder QR decomposition of the matrix X augmented by an n x n zero matrix on top. Using this relation, we derive an algorithm that improves the gram-schmidt downdating algorithm when the columns in the Q factor are not orthonormal. Numerical test results show that the new algorithm produces far more accurate results than the gram-schmidt downdating algorithm far certain ill-conditioned problems.
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