整数环上线性代数方程组的准确解法及软件

ALGORITHMS AND SOFTWARES FOR SOLVING LINEAR ALGEBRAIC EQUATIONS EXACTLY OVER AN INTEGRAL DOMAIN

在许多研究领域和实际计算工作中,要求准确求解线性代数方程组或求矩阵的逆。然而用计算机进行准确运算不仅难度大、耗时长,而且占用相当大的存贮空间。因此,通常代之以近似计算。但近似计算有时能导致一个问题产生实质性的变化。例如,在舍入误差的影响下,我们无法判别机器所显示的零或小量是否真正是零。如果这个量是代表某行列式的值,则一旦误判,问题将产生不仅是量变,而是质变。又如,用了数值不稳定的算法或求解问题属于病态,舍入误差的影响将使结果毫无意义。

Algorithms and softwares for solving linear algebraic equarions exactly over an integraldomain are described systematically. The elimination method, rank-l updating algorithm, cong-ruence algorithm, and mixed radix algorithm are recommended. Recent softwares of the algori-thms are discussed.