摘要
本文主要讨论如何对三对角Toeplitz线性方程组 进行高精度数值求解。由于系数矩阵A这种比较特殊的结构,使得我们可以设计出快速求解 的直接算法。我们将该算法应用到实际例子的计算过程中,发现大部分例子计算效果显著,但部分例子的计算精度还不能达到计算机机器精度。针对这类达不到计算机机器精度的例子,本文将在快速求解三对角Toeplitz线性方程组 的直接算法基础上,进一步进行迭代精化,从而提高这类例子的计算精度。数值实验表明通过迭代精化,我们算法计算精度可以达到计算机机器精度。
This paper mainly discusses how to numerically solve tridiagonal Toeplitz linear systems  efficiently. Since the coefficient matrix A has a special structure, we can design a direct algorithm to quickly solve . We will apply the above algorithm to the calculation of practical examples and find that the calculation precision of some examples is not as high as that of computer's ma-chine accuracy. In order to improve the precision of algorithm, this paper further carries out iter-ative refinement to quickly solve the tridiagonal Toeplitz linear equations of . Numerical experiments show that the computational accuracy of our algorithm can reach computer's machine accuracy by iterative refinement.
出处
《理论数学》
2020年第5期425-432,共8页
Pure Mathematics
基金
2019年硕士研究生校级科研创新项目(CX2019SS34)。
