| 对称系数线性方程组的简化解法 |
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| 引用本文： | 韩立业.对称系数线性方程组的简化解法[J].合肥工业大学学报(自然科学版),1993(4). |
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| 作者姓名： | 韩立业 |
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| 摘 要： | 本文用数学归纳法证明了具有对称系数的线性方程组用高斯消去法求解,每次消元所得之降阶子矩阵仍为对称矩阵,由此引出了一条重要推论:消元过程只需在上三角阵内进行。从而大大减少计算工作量,节省了内存。
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| 关 键 词： | 高斯消去法 简化 对称矩阵 上三角阵 子矩阵 |
A SIMPLIFIED SOLVING PROCESS OF THE LINEAR SIMULTANEOUS EQUATION WITH SYMMETRIC COEFFICIENT |
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| Han Liye.A SIMPLIFIED SOLVING PROCESS OF THE LINEAR SIMULTANEOUS EQUATION WITH SYMMETRIC COEFFICIENT[J].Journal of Hefei University of Technology(Natural Science),1993(4). |
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| Authors: | Han Liye |
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| Abstract: | In this paper,we proved that the submatrix which is obtained from every elimination transformation by Ganssian elimination method in solving linear simultameons equation with symmetric coefficient, is symmetric matrix by mathematical induction.From above, an important inference is produced : All of the elimination transformations are done only in the upper triangular matrix. Thus the calculation efficiency is enhanced greatly and memories of the computer can be saved. |
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| Keywords: | Gaussian eliminaton method symmetric matrix submatrix upper triangular matrix |
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