浙江师范大学学报（自然科学版）
浙江師範大學學報（自然科學版）
절강사범대학학보（자연과학판）
Journal of Zhejiang Normal University(Natural Sciences)
2015年
4期
366-371
,共6页
迭代法%收敛阶%三阶收敛性%重根
迭代法%收斂階%三階收斂性%重根
질대법%수렴계%삼계수렴성%중근
iterative method%convergence order%cubical convergence%multiple root
给出了求非线性方程重根的一类迭代法,证明了这类方法的三阶收敛性,获得了迭代误差,指出了这个类的广泛性,即它包含了一些已知的方法.通过数值例子与一些已知方法进行比较,说明了新方法的有效性,即在某些情形下,新方法比一些已知方法收敛快,且在其他方法发散的情况下新方法还是以很快的速度收敛.
給齣瞭求非線性方程重根的一類迭代法,證明瞭這類方法的三階收斂性,穫得瞭迭代誤差,指齣瞭這箇類的廣汎性,即它包含瞭一些已知的方法.通過數值例子與一些已知方法進行比較,說明瞭新方法的有效性,即在某些情形下,新方法比一些已知方法收斂快,且在其他方法髮散的情況下新方法還是以很快的速度收斂.
급출료구비선성방정중근적일류질대법,증명료저류방법적삼계수렴성,획득료질대오차,지출료저개류적엄범성,즉타포함료일사이지적방법.통과수치례자여일사이지방법진행비교,설명료신방법적유효성,즉재모사정형하,신방법비일사이지방법수렴쾌,차재기타방법발산적정황하신방법환시이흔쾌적속도수렴.
A new family of iterative methods to find multiple roots of a nonlinear equation was obtained.Third order convergence was proved for these methods and iteration errors were given.The generality of the family was presented:the family includes , as particular cases , several well known families and methods.By compa-ring the proposed methods with some other methods through numerical experiments , the robustness and effi-ciency of the new methods were shown.It was showed that the presented methods converge faster than some other methods and even converge very fast at some cases while the other methods diverge.
