矩阵的Crout递归分解算法及程序设计

Recursive Algorithm and Programming for Matrix Crout's Factorization

将矩阵An×n的Crout分解推广到Am×n上,并在常规的迭代算法上加以创新,给出了递归的分解算法。在实现算法的过程中,对数据进行了巧妙的处理,使中间数据及最终计算结果都具有分数形式,不仅使得结果具有绝对的精确度,成功解决了数据的精度问题,而且更符合人们阅读的习惯。经过运行测试,算法设计合理,程序运行高效准确。

Applying Crout's factorization of matrix An×n to matrix Am×n that has m rows and n columns this paper develops a new recursive algorithm of Crout's factorization of matrix on the basis of thorough study of the traditional iterative algorithm. In the realization of algorithm, the data is skillfully dealt, so the interim data and the result have the form of fraction. The advantage is that the results obtained from the method are absolutely exact and the method successfully solves the problem of data's exactness. Besides it conforms to readers' reading habit compared to double or float forms. After running it, the results show that the algorithm is reasonably designed and the program runs at high proficiency and exactness.