UMIST Stability of theDiagonal Pivoting
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چکیده
LAPACK and LINPACK both solve symmetric indeenite linear systems using the diagonal pivoting method with the partial pivoting strategy of Bunch and Kaufman (1977). No proof of the stability of this method has appeared in the literature. It is tempting to argue that the diagonal pivoting method is stable for a given pivoting strategy if the growth factor is small. We show that this argument is false in general, and give a suucient condition for stability. This condition is not satissed by the partial pivoting strategy, because the multipliers are unbounded. Nevertheless, using a more speciic approach we are able to prove the stability of partial pivoting, thereby lling a gap in the body of theory supporting LAPACK and LINPACK.
منابع مشابه
UMIST Stability of the Diagonal Pivoting Method with Partial
LAPACK and LINPACK both solve symmetric inde nite linear systems using the diagonal pivoting method with the partial pivoting strategy of Bunch and Kaufman (1977). No proof of the stability of this method has appeared in the literature. It is tempting to argue that the diagonal pivoting method is stable for a given pivoting strategy if the growth factor is small. We show that this argument is f...
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Stability of the Diagonal Pivoting Method with Partial Pivoting
LAPACK and LINPACK both solve symmetric indefinite linear systems using the diagonal pivoting method with the partial pivoting strategy of Bunch and Kaufman [Math. Comp., 31 (1977), pp. 163–179]. No proof of the stability of this method has appeared in the literature. It is tempting to argue that the diagonal pivoting method is stable for a given pivoting strategy if the growth factor is small....
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LAPACK and LINPACK both solve symmetric indeenite linear systems using the diagonal pivoting method with the partial pivoting strategy of Bunch and Kaufman (1977). No proof of the stability of this method has appeared in the literature. It is tempting to argue that the diagonal pivoting method is stable for a given pivoting strategy if the growth factor is small. We show that this argument is f...
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