Computational Experience with Rigorous Error Bounds for the Netlib Linear Programming Library
Computational Experience with Rigorous Error Bounds for the Netlib Linear Programming Library
复制标题
Netlib 线性规划库具有严格误差范围的计算经验
作者：
C. Keil;C. Jansson
Netlib 线性规划问题库是一个众所周知的套件，其中包含许多现实世界的应用程序。最近 Ordóñez 和 Freund 表明，这些问题中 71% 是病态的。因此，可能会出现数值困难。在这里，我们展示了该库的严格结果，这些结果是通过使用区间算术的验证方法计算得出的。除了这些问题的原始输入数据外，我们还考虑区间输入数据。计算出的严格边界和算法的性能与到下一个不适定线性规划问题的距离有关。
The Netlib library of linear programming problems is a well known suite containing many real world applications. Recently it was shown by Ordóñez and Freund that 71% of these problems are ill-conditioned. Hence, numerical difficulties may occur. Here, we present rigorous results for this library that are computed by a verification method using interval arithmetic. In addition to the original input data of these problems we also consider interval input data. The computed rigorous bounds and the performance of the algorithms are related to the distance to the next ill-posed linear programming problem.