@MISC{Chang99mathematikcomponentwise, author = {Xiao-wen Chang and Christopher C. Paige}, title = {Mathematik Componentwise perturbation analyses}, year = {1999} }
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Abstract
Summary. This paper gives componentwise perturbation analyses for Q and R in the QR factorization A = QR, QTQ = I, R upper triangular, for a given real m × n matrix A of rank n. Suchspecific analyses are important for example when the columns of A are badly scaled. First order perturbation bounds are given for both Q and R. The analyses more accurately reflect the sensitivity of the problem than previous such results. The condition number for R is bounded for a fixed n when the standard column pivoting strategy is used. This strategy also tends to improve the condition of Q, so usually the computed Q and R will both have higher accuracy when we use the standard column pivoting strategy. Practical condition estimators are derived. The assumptions on the form of the perturbation ∆A are explained and extended. Weaker rigorous bounds are also given. Mathematics Subject Classification (1991): 15A23, 65F35 1