中文摘要：

研究n维空间中m个点的最小闭包球（MEB）问题。通过结合确定并删除内部点的技术到序列最小最优化（SMO）方法中,提出一种近似求解MEB问题的改进的SMO-型算法。证明了该算法具有线性收敛性。数值结果表明对于一些mn的大规模数据集,改进的算法与原算法相比速度可以提高10倍以上。尤其,当n等于100且m等于100000时,改进的SMO-型算法仅需执行8s。此外,对于n等于10000且m等于1000的大规模数据集,改进的算法也仅需执行150s。

英文摘要：

To study the Minimum Enclosing Bal（lMEB）problem of m points in n dimensions. By incorporating the technique of identification and elimination of interior points into Sequential Minimal Optimization（SMO）method, a modified SMO-type algorithm for the MEB problem is presented. This algorithm has the linear convergence. The numerical results show that the CPU time of the modified algorithm may improve by more than a speed-up factor of 10 on some large-scale date sets where m》n . In particular, when n equals 100 and m equals 100 000, the modified SMO-type algorithm only needs to run about 8 s. In addition, it also takes only about 150 s for the large-scale data sets in which n equals 10 000 and m equals 1 000.