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一族求解非线性方程的高阶迭代方法 被引量：1

A family of iterative methods with higher order convergence for nonlinear equations
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摘要 给出了一族解非线性方程的具有高阶收敛速度的迭代方法.该方法不仅包含了文献中的十六阶迭代方法,而且还给出了新的十六阶迭代方法.最后,通过数值算例验证了方法的有效性和可行性. In this paper,a new family of iterative methods for solving nonlinear equations with high order convergence was discussed.This method not only contained the sixteen-order iteration of the literature,but also gave the new sixteen-order iterative method.Finally,the numerical experiments verified the feasibility and effectiveness of the method.
作者 皮丽敏 潘状元
机构地区 哈尔滨理工大学应用科学学院
出处 《哈尔滨商业大学学报（自然科学版）》 CAS 2012年第6期751-753,768,共4页 Journal of Harbin University of Commerce：Natural Sciences Edition
关键词 非线性方程 迭代方法 牛顿方法 收敛阶 nonlinear equations iterative methods Newton＇s method convergence
分类号 O175 [理学—基础数学]
  • 相关文献

参考文献9

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同被引文献7

  • 1J.Xu,B.Han,L.Li.Frozen Landweber Iteration for Nonlinear Ill-Posed Problems[J].Acta Mathematicae Applicatae Sinica,2007,23(2):329-336. 被引量：8
  • 2DENG Y J,LIU Z H.New fast iteration for determining surface temperature and heat flux of general sideways parabolic equation[J].Nonlinear Anal.Real World Appl.,2011,12(1):156-166.
  • 3ZHENG G H,WEI T.Two regularization methods for solving a Riesz-Feller space-frational backward diffusion problem[J].Inverse Problems,2010,26:1-22.
  • 4JIN Q N.On a regularized Levenberg-Marquardt method for solving nonlinearinverse problems[J].Numer.Math.,2010.115:229-259.
  • 5YANG Q Q,LIU F W,TURNER I.Numerical methods for fraction partial differential equations with Riesz space fractional derivatives[J].Appl Math Model.,2010,34:200-218.
  • 6HANKE M.Accelerated Landweber Iterations for the Solution of Ill-Posed Equations[J].Numer.Math,1991,60 (1):341-373.
  • 7韩波,刘家琦,后步风.非线性不适定算子方程算子与右端项皆有扰动的Landweber迭代法[J].计算数学,2002,24(4):479-486. 被引量：5

引证文献1

哈尔滨商业大学学报（自然科学版）
2012年 第6期

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