摘要
本文对不适定的线性方程组给出一种求解方法．给出了相对优解的定义，证明相对优解的存在性与唯一性，进而构造了ｎ维欧氏空间上一个连续泛函，证明该泛函的极值问题解的存在性和唯一性．并利用泛函极值问题的解给出不适定线性方程组相对优解的近似解和近似解收敛于相对优解的证明．
This paper abtained a kind of solution method of improperly Posed systemof linear aquations. It also offerd the definition of relative superior solution and proved theexistence and uniquenss of the relative superior solution. Furthermore, a continuous functional is formed on n-dimensional euclidean space and the existence and uniqueness of solution of its extrmum problems were proved. By using this solution of functional extremum,the paper obtains that the relative superior solution of improperly Posed system of linearequations has its approximate solution and proves that the approximate solution convergesto relative superior solution.
关键词
相对优解
线性方程组
解
存在性
近似解
relative superior solution positivity of the operator equation the method of lagrange uncertain factor
