| 方程求根的Hermite抛物插值法 |
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| 引用本文： | 姜儒明.方程求根的Hermite抛物插值法[J].大连铁道学院学报,1989,10(1):1-6. |
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| 作者姓名： | 姜儒明 |
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| 作者单位： | 大连铁道学院数学教研室 |
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| 摘 要： | 本文提出了方程求实根的一个 Hermite 抛物插值法,并论证了它的收敛性,敛速为1+2~(1/2)阶.若所求根为二重根(重数未知),则敛速为1/2+(3(1/2))/2阶.若将所得公式与牛顿求根公式复合,则有5阶的敛速;若所求根为二重根,则复合法有1.5阶的敛速.
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| 关 键 词： | 非线性方程 Hermite 二重根 插值法 |
Hermitian Parabolic Interpolation Method for Solving Nonlinear Equations |
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| Jiang Ruming.Hermitian Parabolic Interpolation Method for Solving Nonlinear Equations[J].Journal of Dalian Railway Institute,1989,10(1):1-6. |
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| Authors: | Jiang Ruming |
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| Institution: | Jiang Ruming |
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| Abstract: | An iteration method is derived from Hermitian parabolic interpolation for solving nonlinear equation numerically.The sequence derived from the iteration method converges and has 1+ 2~1/2 order convergence.If the mentioned numerical method is used to find a real double root, and its multiplicity is unknown,the obtained sequence comerges and has 1/2+(~21/2)/3 order vergence.If the given iteration method combines with Newton's method,an iteration method of the 5 order convergence is obtained.The compound method is also used to find a real double root,and the iterative process has 1.5 order convergence. |
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| Keywords: | Hermite interpolation non-linear equation exponent convergence/real double root compound method effective exponent convergence order |
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