THE Effects of Rounding Error on an Algorithm for Downdating a Cholesky Factorization.
MARYLAND UNIV COLLEGE PARK DEPT OF COMPUTER SCIENCE
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Let the positive definite matrix A have a Cholesky factorization A RtransposedR. For a given vector x suppose that A A - xxtransposed has a Cholesky factorization A RtransposedR. This paper considers an algorithm for computing R form 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 R can be a very ill-conditioned function of R and x. Author
- Statistics and Probability