特征值问题的一种数值验算方法

A Numerical Verification Method for Eigenvalue Problem

针对椭圆型方程的特征值问题,提出一种数值验算的方法,验证特征对的存在性,并得出特征值所在的区间范围。主要的方法是将特征对转化为一个泛函的不动点,然后在计算机上构造一个"候补"的集合,利用Schauder不动点定理,证明在这个集合上存在不动点。最后有两个数值验算的结果。

A numerical verification method is proposed for eigenvalue problem of elliptic operators. It verifies the existence of the eigenpair and obtains the interval where the eigenvalue exists. The main way is to transfer the eigenpair to a functional＇s fixed point, and to build a ＇candidate＇ set to prove the existence of a fixed point in it by the Schauder fixed point theorem by using a computer. Finally the findings are illustrated by two numerical examples.