| 不适定的线性方程组的求解方法 |
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| 引用本文： | 胡长华. 不适定的线性方程组的求解方法[J]. 天津师范大学学报(自然科学版), 1996, 0(2) |
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| 作者姓名： | 胡长华 |
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| 作者单位： | 天津汽车工业集团有限公司职工大学 |
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| 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．
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| 关 键 词： | 相对优解，算子方程的适定性，拉格朗日不定因子法 |
METHODS FOR SOLVING OF IMPROPERLY POSED SYSTEM OF LINEAR EQUATIONS |
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| Hu Changhua. METHODS FOR SOLVING OF IMPROPERLY POSED SYSTEM OF LINEAR EQUATIONS[J]. Journal of Tianjin Normal University(Natural Science Edition), 1996, 0(2) |
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| Authors: | Hu Changhua |
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| Abstract: | 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. |
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| Keywords: | relative superior solution positivity of the operator equation the method of lagrange uncertain factor |
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