| 摘要: |
| 在数值分析中Broyden方法具有一个非常重要的性质，即用它求解n维线性方程组时，至多2n步就能达到精确解。笔者研究了将该方法用于求解线性方程组时的内在性质，否定了一个自然的推测，指出它在解线性方程组时不是一个下降的算法，即所得到的点列与方程组的解之间的距离在任何向量范数意义下都不具有单调下降性。 |
| 关键词: Broyden方法 线性方程组 下降算法 |
| DOI： |
| 修订日期：2000-06-18 |
| 基金项目: |
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| A Note on Broyden''''s Method |
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| Abstract: |
| Broyden's methods are one of the most important methods in numerical analysis. There is an essential nature that the algorithms terminate in at most 2 n steps on linear problems with n variables. The property of the algorithms on linear problems is studied and the Broyden's methods have been proved that they are not descant. More precisely, the distances between the sequences obtained by solving the linear problems and the solutions of the linear problems do not decrease under any vector norm. |
| Key words: linear equations,Broyden's method,descant algorithms |
