压缩映射原理及其应用

The CompressionMapping Principle and Its Application

在各类方程的求解问题里常转化为求映射的不动点,利用逐次逼近法求不动点,在计算数学有广泛的应用。利用度量空间及压缩映射的观点来描述这一方法,再给出它的一些应用。

The solving problems of various equations are usually transformed to the solving problems of the fixed points in mapping, and the successive-approximation method is widely used to solve the problems of fixed points. The paper describes this method from the point of metric space and compression-mapping, and presents some of its applications.