| 线性方程组ATAx=b的结构向后误差 |
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| 引用本文： | 孙继广. 线性方程组ATAx=b的结构向后误差[J]. 黑龙江大学自然科学学报, 2004, 21(4): 4-10 |
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| 作者姓名： | 孙继广 |
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| 作者单位： | Ume(a)大学,计算科学系,S-901 87 Ume(a),瑞典 |
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| 基金项目： | Supported by the Swedish Strategic Research Foundation Grant (Matrix Pencil Computations in Computer-Aided Control System Design: Theory，Algorithms and Software Tools) |
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| 摘 要： | 设A是一个列满秩矩阵,x是线性方程组ATAx=b的一个计算解.基于这一方程组的系数矩阵ATA具有特殊的结构,定义了x的一个结构向后误差ηs(x),并且利用Brouwer不动点定理和奇异值分解,给出了这个结构向后误差ηs(x)的上、下界.计算实例表明这个被获得的ηs(x)的上、下界,为检验线性方程组ATAx=b的计算解的结构向后稳定性,提供了一个简便的方法.
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| 关 键 词： | 线性方程组 向后误差 结构向后误差 结构向后稳定性 |
Structured backward error for the linear system ATAx= b |
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| Ji-guang Sun. Structured backward error for the linear system ATAx= b[J]. Journal of Natural Science of Heilongjiang University, 2004, 21(4): 4-10 |
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| Authors: | Ji-guang Sun |
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| Abstract: | Let A be a matrix of full column rank, and let x be a computed solution to the linear system ATAx = b. As the coefficient matrix ATA of the system has a special structure, a structured backward error (SBE) ηs(x) of x is defined, and upper and lower bounds for the SBE ηs(x) are given by applying the Brouwer fixed-point theorem and the singular value decomposition. Numerical examples show that the bounds porvide a convenient way of testing the structured backward stability of computed solutions to the linear system ATAx = b. |
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| Keywords: | linear system backward error structured backward error structured backward stability |
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