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IMA Journal of Applied Mathematics 1979 23(2):203-213; doi:10.1093/imamat/23.2.203
© 1979 by Institute of Mathematics and its Applications
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The Effects of Rounding Error on an Algorithm for Downdating a Cholesky Factorization

G. W. STEWART

Department of Computer Science, University of Maryland

Let the positive definite matrix A have a Cholesky factorizationA = RTR. For a given vector xsuppose that à =A - xxT has a Cholesky factorization à = T.This paper considers an algorithm for computing from R and x and an extension for removing a row from the QR factorization of a regression problem. It is shown that the algorithm is stable in the presence of rounding errors. However, it is also shown that the matrix can be a very ill-conditioned function of R and x.


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