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中文摘要：
Banach空间中的闭球族称为球覆盖，如果任一元素的内部不含原点，且所有元素之并覆盖了单位球面．本文采用神经网络方法研究R中球覆盖最小半径的计算问题，重新给出计算基数为m（≥n＋1）的球覆盖最小半径的公式（对于m=2n（对称）和m=n＋1给出了解析表达式），然后基于罚函数法建立神经网络模型，该模型的平衡点集具有大范围吸引性且（渐近）稳定平衡点等价于（严格）极大值点．最后给出了数值例子验证该方法的有效性．
英文摘要：
A collection of closed balls in a Banach space is called a ball-covering,if its union contains the unit sphere and the interior of each member is off the origin. This paper considers the minimum radius problem of ball-coverings with the cardinality m（≥n＋ 1） in n by the neural network method. It gives a new computing formula for the minimum radius（and the exact minimum radius for m = 2n and n＋ 1）, then, based on the penalty method, presents a neural network which is globally convergent and the solution is approximated. Numerical examples are given to demonstrate further the effectiveness of the method.
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