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STABILITY OF THE DIAGONAL PIVOTING METHOD WITH PARTIAL PIVOTING.
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- المؤلفون: Higham, Nicholas J.1
- المصدر:
SIAM Journal on Matrix Analysis & Applications. 1997, Vol. 18 Issue 1, p52-65. 14p.
- الموضوع:
- معلومة اضافية
- نبذة مختصرة :
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. We show that this argument is false in general and give a sufficient condition for stability. This condition is not satisfied by the partial pivoting strategy because the multipliers are unbounded. Nevertheless, using a more specific approach we are able to prove the stability of partial pivoting, thereby filling a gap in the body of theory supporting LAPACK and LINPACK. [ABSTRACT FROM AUTHOR]
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