应用ABS算法求解一类不定线性方程组

ABS algorithms for solving certain system of indefinite equations

运用ＡＢＳ算法讨论了等式约束优化问题中的拉格朗日乘子法所形成的线性方程 组的求解问题；利用 ＡＢＳ算法的隐式 ＬＱ分解，通过有限步迭代求出原问题变量 的解，同时形成求解乘子的上三角系数阵的方程；给出了算法的具体过程，分析其数 值稳定性和计算量；作为特例，将最小二乘问题的法方程化为文中方程形式，并给出 了一种计算方法。

The solution of indefinite equations arising from quadratic programming with equality constraints are discussed by ABS algorithms. The implicit LQ factorization of ABS method is used, and the detailed procedure of the algorithm is given to solve variables of original problem in finite iterations, and to form the upper triangle coefficient matrix equations for multipliers at the same time. It also discusses the application on the least square solution of a linear system.