大型线性代数方程组解法的探讨

A Method for Solving Large Size Linear Algebraic Equations

针对Saint Venant方程组离散后所形成的线性代数方程组的求解问题 ,将Gauss列主元消去法与压缩存贮技术相结合 ,提出了存贮单元少、舍入误差小且数值计算稳定的计算方法 ,使得河网非恒定流的数值计算更加高效 ,并且计算的精度可得到充分的保证 .

Two kinds of methods are commonly used for solving large size linear algebraic equations which are derived from Saint Venant equations:one is the elimination method,and another is the double sweeping method.Two methods,however,have the disadvantage that they would fail when the denominator is zero or machine zero.This paper proposes a method which combines the Gauss main element elimination method with compress storage technique to solve the equations more efficiently and accurately.The application of the method to a large network proves that it is an efficient method with less storage requirement,small rounding off error and high stability.