一类分块矩阵方程的广义逆求解方法

The Generalized Inverse Computing Method of a Class of Block Matrixequations

摘要: 本文讨论了一类分块矩阵的广义逆，利用分块矩阵的减号逆，给出了一类特殊矩阵方程的求解公式。基于减号逆的性质，结合分块矩阵的运算，给出了一类2 × 2分块矩阵的广义逆的计算过程，探讨了利用初等变换法求解一类分块矩阵的广义逆的方法，并应用于方程组的求解。最后给出了数值计算例子，并将2 × 2分块矩阵的广义逆的计算方法推广应用到了一类特殊的4 × 4分块矩阵的情形。

Abstract: In this paper, the generalized inverse of a class of block matrix is discussed. By using the minus inverse of block matrix, the solution formula of a special matrix equation is given. Based on the properties of the minus inverse and the block matrix operation, the calculation process of the generalized inverse of a class of 2 × 2 block matrices is presented. And the method of solving the generalized inverse of a kind of block matrix by elementary transformation method is discussed. Then the method is applied to solving the equations. Finally, a numerical example is discussed, and the generalized inverse of 2 × 2 block matrix is extended to a special case of 4 × 4 block matrix.