加权α-β广义逆的定义及其计算方法

文中引入对正定算子M、N的加权a-β广义逆。而且给出了此广义逆的一些性质。然后又得到了几个计算该加权a-β广义逆的迭代方法。而且这些迭代条件教师充分必要的。如果a、β为欧几里德范数，而且M=N=I，那么此加权a-β广义逆就变为一般的广义逆A^ 。这样[8]中的结果就是该文的特殊情形。在文章的最后，给出了一个数值例子，还验证了一些性质。

The Definition and Computing Methods of Weighted α-β Generalized Inverse

In this paper, the weighted α-β generalized inverse are introduced with the positive definite operators M and N. Some properties of the weighted α-β generalized inverse are showed. And we will give the iterative methods for computing the weighted α-β generalized inverse and the sufficient and necessary conditions are obtained. If α,β are the Euclidean norms, and M=N=I then the weighted α-β generalized inverse reduces to A+. So all the conclusions in this paper can apply to Moore-Penrose inverse. And the results in [8] are the special case of this methods.A numerical example to illustrate the iterative methods for computing A+α,β is given in the end. That is the special case of M=N=I. From the example some properties of projectors and α-β generalized inverse can be found.