矩阵奇异值分解与非齐次线性方程组系数矩阵的广义逆求解

Singular Value Decomposition of Matrix and Generalized Inverse Solution of Coefficient Matrix of Inhomogeneous Linear Equations

非齐次线性方程组在多数实际工程反演问题中较为常见,对其进行有效地求解是解决实际反演问题的关键,本文通过对方程组系数矩阵进行奇异值分解,推导非齐次线性方程组系数矩阵的广义逆求解过程,给出具体的求解方法和实现步骤,使得求解算法更容易进行计算机编程.

Inhomogeneous linear equations often appear in most practical engineering inversion problems.To solve them effectively is the key for the actual inversion problems.In this paper,the singular value decomposition of the coefficient matrix of equations is carried out.And the generalized inverse solving procedure of coefficient matrix of inhomogeneous linear equations is derived.Further more,the specific solution method and implementation steps are given,which makes the solution algorithm easier to be programmed by computer.