线性方程组的矩阵求解算法

The Algorithm of Matrix in Solving System of Linear Equations

设计的算法是 ,在约当消元法的基础上 ,只需对行最简形矩阵进行删除行和列、增加行、交换行等运算即可得到方程组的通解 .本算法的独特之处是 ,消元过程结束后 ,不需指定自由变量和非自由变量 ,不需写出由自由变量表示非自由变量的具体表达式 ,利用行最简形矩阵求通解时 ,再不需进行乘法和加法运算 ,因而不会增加算法的精度损失量 ,并且由于算法中的运算对象只有矩阵 ,因而算法简单 。

The algorithm in this article is designed on the basis of the elimination of Jordan. General solution can be (obtained) merely by operation like eliminating, adding or altering row and line of the matrix in its most simplifying form. The particular advantage of the algorithm is that we don't have to list out either the free and non-free variant, or their specific equation. Since no multiplication and addition are involved, the accureccy of the approach will be greatly increased. Moreover, the result is much more accessable for we have only matrix involved in the process.