求解一个整数方程的新解法

A New Approach to an Integeral Equation

ni=1aixi =p是一个由实验数据问题抽象而出的整数方程求非负整数解的数学模型 .为了使该问题实现计算机求解的可能 ,本文首先将原问题转化为讨论一类整数规划最优解问题 .从对应松弛规划问题的目标函数值为 0的最优解出发 ,根据舍入凑整法原则 ,再次将问题转化为另一简化后的整数方程 ,这样大大缩小了解的范围 ,及进一步迅速降低了方程右端的 p值 。

The integeral equation ∑ni=1a ix i=p is model for the n onnegative integer solutions of the integeral equation abstracted from some prob lems about experimental data. In this paper, the original problem is transformed into discussing a kind of optimal problems of integer programming, by the disscuss of the corresponding relaxaction programming problem, and the existence dom ain of the solutions of the original equation is reduced.Therefore, the original integeral equation can be solved by computer.