| 计算方程重根及其重数的算法 |
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| 引用本文： | 管宇. 计算方程重根及其重数的算法[J]. 大学数学, 2008, 24(2): 78-81 |
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| 作者姓名： | 管宇 |
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| 作者单位： | 浙江林学院,应用数学系,浙江,临安,311300 |
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| 摘 要： | 给出一种计算方程重根及重数的迭代算法,分别具有平方收敛和线性收敛.(i)迭代:x_(n+1)=x_n-f x_n (f'(x_n))/((f'(x_n))~2-(f(x_n)f~n(x_n)),m_n=((f'(x_n)))~2/((f'(x_n))~2-f(xn_)f″(x_n)),n=0,1,2,…,重数m≈mn;(ii)加速迭代:x_(n+1)=x_n-(f~((m-1))(x_n))/(f(~m)(x_n)).
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| 关 键 词： | 重根 重数 迭代算法 收敛阶 |
An Iteration Algorithm of Finding Multiple Roots And Its Multiplicity of Equation in One Variable |
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| GUAN Yu. An Iteration Algorithm of Finding Multiple Roots And Its Multiplicity of Equation in One Variable[J]. College Mathematics, 2008, 24(2): 78-81 |
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| Authors: | GUAN Yu |
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| Abstract: | This paper gives an iteration algorithm of finding multiple roots and its multiplicity of equation in one variable,their convergence order are 2 and 1 separately:(i)iteration x_(n+1)=*x_n-f x_n (f'(x_n))/((f'(x_n))~2-f(x_n)f~n(x_n)),m_n=(f')(x_n)))~2/((f'(x_n))~2-f(xn_)f″(x_n)),n=0,1,2,…,the multiplicity m≈mn.(ii)accelerating convergence x_(n+1)=x_n-(f~((m-1))(x_n))/(f(~m)(x_n)). |
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| Keywords: | multiple root multiple number iterative algorithm convergence order |
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