线性方程组迭代解法的另类矩阵形式

Another Shape of Iterative Methods for Linear Equations

改进了线性方程组迭代解法的矩阵形式，以最简单的Jaeobi迭代法的迭代矩阵为基础，只需经过简单的加减和数乘运算就可得到Seidel和SOR的迭代过程，使得算法新形式的求解过程数学意义非常明确，表达形式也非常简洁，这样不仅便于理解记忆，还非常有利于编程实现。改进后的矩阵迭代形式求解计算量为：Seidel需要大约n^2次乘除法，SOR约为2n^2次乘除法。且改进后的Seidel迭代法和SOR方法存储空间也较传统形式为岁。

the paper improved the shape that describes iterative methods for linear equations by combining the proficiency of general formulas and the concision of matrix. The Seidel and SOR iterative processes can be achieved by simple operations of adding, subtracting and multiplying which make the mathematic significance of creative solution procedure in this improved algorithm definite, and expression form brief. This is convenient not only for students to comprehend and remember the knowledge, but also for the programers to carry out the operations. The computational complexities of the improved iteration form of matrix are： n^2multiply-divides in Seidel iteration, 2n^2multiply-divides in SOR iteration. At last, less storage space is needed in the improved Seidel and SOR iterative methods to traditional methods.