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Accurate downdating of least squares solutions. (English) Zbl 0811.65034
Solutions to least squares problems can be obtained from the $$QR$$ decomposition of the corresponding data matrix $$X$$. When a complete $$QR$$ factorization of the matrix $$X$$ is available, the $$R$$ factor can be modified to give the $$QR$$ decomposition of the modified data matrix $$\widetilde X$$, where either a new observation row is added (updating) or an old observation is deleted (downdating).
Algorithms that only downdate $$R$$ and do not store $$Q$$ require less operations. However, they do not give good accuracy and may not recover accuracy after an ill-conditioned problem has occurred. The authors present a new accurate downdating algorithm using corrected seminormal equations (CSNE) and a hybrid downdating algorithm to switch between the CSNE algorithm and the LINPACK downdating algorithm. Numerical tests and comparisons are presented.

##### MSC:
 65F20 Numerical solutions to overdetermined systems, pseudoinverses
LINPACK
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