Stability of the Diagonal Pivoting Method with Partial Pivoting
Stability of the Diagonal Pivoting Method with Partial Pivoting
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DOI：
10.1137/s0895479895290371
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发表时间：
1997
期刊：
影响因子：
--
通讯作者：
N. Higham
中科院分区：
文献类型：
--
作者：
N. Higham
LAPACK和LINPACK都使用对角枢转方法和Bunch和考夫曼的部分枢转策略来求解对称不定线性系统[Math. Comp.，第31卷（1977年），第102页。163- 179]。在文献中没有出现该方法稳定性的证据。这是诱人的认为，对角线旋转方法是稳定的一个给定的旋转策略，如果增长因子是小的。我们证明了这一论点在一般情况下是错误的，并给出了稳定性的充分条件。部分主元策略不满足这个条件，因为乘数是无界的。然而，使用更具体的方法，我们能够证明部分枢转的稳定性，从而填补了支持LAPACK和LINPACK的理论体系中的空白。
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.