新疆大学学报(自然科学版)
新疆大學學報(自然科學版)
신강대학학보(자연과학판)
XINJIANG UNIVERSITY JOURNAL(NATURAL SCIENCE EDITION)
2010年
1期
51-55
,共5页
何翠杰%阿布都热西提·阿布都外力
何翠傑%阿佈都熱西提·阿佈都外力
하취걸%아포도열서제·아포도외력
牛顿方法%非线性方程组%三步迭代方法%效率指标
牛頓方法%非線性方程組%三步迭代方法%效率指標
우돈방법%비선성방정조%삼보질대방법%효솔지표
Newton's method%Nonlinear equations%Three-step iterative method%Efficiency index
本文给出求解非线性方程组具有六阶精度的三步迭代方法,理论上给予了证明.并且与Jae Heon Yun提出的有四阶精度的三步迭代方法相比有比较大的改进.最后给出数值例子,对几种不同的迭代方法进行比较,数值结果显示给出的方法与理论结果一致.
本文給齣求解非線性方程組具有六階精度的三步迭代方法,理論上給予瞭證明.併且與Jae Heon Yun提齣的有四階精度的三步迭代方法相比有比較大的改進.最後給齣數值例子,對幾種不同的迭代方法進行比較,數值結果顯示給齣的方法與理論結果一緻.
본문급출구해비선성방정조구유륙계정도적삼보질대방법,이론상급여료증명.병차여Jae Heon Yun제출적유사계정도적삼보질대방법상비유비교대적개진.최후급출수치례자,대궤충불동적질대방법진행비교,수치결과현시급출적방법여이론결과일치.
We proposed two three-step iteration methods for solving system of nonlinear equations and it is showed that the methods have sixth-order convergence. Compared with Jae Heon Yun. [J.H.Yun, a note on three-step iterative method for nonlinear equation, Appl Math Comput, 2008, 202: 401-405] proposed three-step iterative method with fourth-order convergence, our methods have a significant improvement.Some numerical experiments are given to illustrate the performance of our three-step iterative method.