| 伪谱的边界曲线及其跟踪算法的步长控制 |
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| 引用本文： | 刘颖,白峰杉.伪谱的边界曲线及其跟踪算法的步长控制[J].高等学校计算数学学报,2003,25(1):1-11. |
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| 作者姓名： | 刘颖 白峰杉 |
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| 作者单位： | 清华大学数学科学系,北京,100084 |
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| 摘 要： | 1 引言 1990年L.N.Trefethen为度量矩阵的非正规性引入了矩阵的伪谱,对于任意的ε≥0,矩阵A∈C~(n×n)的ε-伪谱定义为 ∧_ε(A)={z:z∈σ(A △A),||△A||≤ε},其中σ(·)表示矩阵的特征值集合(谱集合),||·||表示矩阵的2-范数。利用预解式(zI—A)~(-1),
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| 关 键 词： | 伪谱 边界曲线 跟踪算法 步长控制 矩阵 复平面 梯度 牛顿迭代 |
THE BOUNDARY CURVE OF PSEUDOSPECTRUM AND THE STEPSIZE CONTROL OF CURVE TRACING ALGORITHM |
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| Liu Ying Bai Fengshan.THE BOUNDARY CURVE OF PSEUDOSPECTRUM AND THE STEPSIZE CONTROL OF CURVE TRACING ALGORITHM[J].Numerical Mathematics A Journal of Chinese Universities,2003,25(1):1-11. |
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| Authors: | Liu Ying Bai Fengshan |
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| Abstract: | The boundary curve of the pseudospectrum is defined as a contour line of its resolvent norm. The curve tracing algorithm is a rather simple continuation method, which determines this curve by a prediction-correction scheme. But this algorithm can not deal with the bifurcation point where the resolvent norm is not differentiable. Due to this defect in this paper we investigate the smoothness of boundary curve, and give a method of stepsize control which can deal with bifurcation points. Numerical results are also presented. |
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| Keywords: | pseudospectrum stepsize control |
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