| 奇异点处的拟Newton方法 |
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| 引用本文： | 席少霖,顾明. 奇异点处的拟Newton方法[J]. 计算数学, 1988, 10(3): 291-298 |
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| 作者姓名： | 席少霖 顾明 |
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| 作者单位： | 北京计算机学院(席少霖)，南京航空学院(顾明) |
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| 摘 要： | 1.引言 假定F是R~m→R~m的可微映射,x~*∈R~m是 F(x)=0 (1.1)的解. 如果在解点处Frechet导数是可逆的,只要F′(x)具有一定的性质,就可保证Newton迭代 x_(i+1)~N=x_i~N-F′(x_i~N)~(-1)F(x_i~N) i=0,1,… (1.2)产生的点列在||x_0-x~*||适当小时二阶收敛于x~*:
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QUASI--NEWTON METHODS AT SINGULAR POINT |
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| Affiliation: | Xi Shao-lin Beijing Computer Institute Gu Ming Nanjing Aeronautical Institute |
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| Abstract: | If employed to find a root, x, of nonlinear equations F(x) = 0 in R~m withthe Jacobian F'(x) being singular at that root, the quasi-Newton methods areshown to yield sequences that converge linearly to x if the initial guess is chosenin a special region. Modified methods are also given to obtain a better convergencerate. |
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