奇摄动线性代数方程组及其对病态方程的应用
Singular Perturbation of Linear Algebraic Equations with Application to Stiff Equations
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摘要: 本文首先从一个曲柄导杆机构的优化问题提出了含小参数线性代数方程组的奇摄动问题。然后利用摄动方法证明了这个问题解的存在唯一性,同时给出了解的渐近展开和误差估计。最后讨论了所得结果对求解病态方程的应用。Abstract: In this paper the singular perturbation problem of linear algebraic equations with a small parameter is presented by an example in practice.The existence and uniqueness theorem of its solution is proved by the perturbation method and the estimation of error for its approximate solution is given.Finally,the example mentioned above explaining how to apply the theory to solve the stiff equations is shown.
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[1] Nayfeh,A.H.,Introduction to Perturbation Techniques,John Wiley and Sons,New York(1981). [2] 曹志浩、张玉德、李瑞遐编,《矩阵计算和方程求根》,高等教育出版社(1984). [3] J.M,奥特加著(张丽君等译),《数值分析》,高等教育出版社(1983). -
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