求解拟五对角线性方程组的两参数法  

Tow Parameters Algorithm for Solving the Quasi-pentad-diagonal Linear Equations Set

作　　者：李文强[1] 张海霞[1] 李卫霞[2] 

机构地区：[1]河南师范大学数学与信息科学学院,河南新乡453007 [2]河南师范大学附属中学,河南新乡453007

出　　处：《科技导报》2011年第7期55-57,共3页Science & Technology Review

摘　　要：针对拟五对角线性方程组的特点,选择最后两个未知量xn-1和xn作为参数(两参数法),将它们代入其他n-2个方程中,从而将原方程组的求解问题转化为求解3个五对角线性方程组,然后再求出参数xn-1和xn,最终求出全部解向量。由于算法的主要运算是运用追赶法求解五对角线性方程组,具有较好的数值稳定性。数据实验表明,与四参数算法相比,两参数法不仅速度快,对同阶的线性方程组求解时间比约为1.47,内存开销也比四参数法少。该算法需要的乘除次数为O(23n),加减次数为O(16n),内存占用量约为O(10n)。算术运算次数和内存占用量均与n呈线性关系。An algorithm is presented for solving quasi quinque-diagonal linear system of equation.First,the last two variables are selected as the parameters and are put into the other n-2 equations.Then the original problem can be transformed into a problem for solving three quinque-diagonal linear systems of equation.Finally,all the solution vectors can be obtained by solving the parameters xn-1 and xn.A forward elimination and backward substitution algorithm is used to solve the quasi quinque-diagonal linear system,it shows a good numerical stability.Experimental data indicate that comparing with the four parameter algorithm,not only the two parameter method is fast for solving the same order of linear equations with time ratio of about 1.47,but also the memory consumption is less than that used by the four parameters.The measure of multiplication or division in this algorithm is O（23n） and O（16n） for addition and subtraction,respectively.The memory needed is about O（10n）.The number of arithmetical operations and memory consumption all have a linear relation with the n.

关 键 词：拟五对角线性方程组 拟五对角矩阵 参数法 追赶法 

分 类 号：O241.6[理学—计算数学]