Convergence on the iteration of Halley family in weak conditions 被引量：19

Convergence on the iteration of Halley family in weak conditions

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摘要 WE have obtained the convergence theorems of the iteration of Halley family by the point estimate of Smale. In the point estimate, map f which is desired to be solved is presumed to be analytic in some proper neighborhood at the initial value z<sub>0</sub>. From the viewpoint of

作者 WANG XinghuaDepartment of Mathematics, Hangzhou University, Hangzhou 310028, China

出处《Chinese Science Bulletin》 SCIE EI CAS 1997年第7期552-555,共4页

关键词 OPERATOR equations Banuch space the ITERATION of HALLEY FAMILY CONVERGENCE WEAK conditions. operator equations Banach space the iteration of Halley family convergence weak conditions

分类号 O177 [理学—基础数学]

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参考文献8

1王兴华,韩丹夫.ON DOMINATING SEQUENCE METHOD IN THE POINT ESTIMATE AND SMALE THEOREM[J].Science China Mathematics,1990,33(2):135-144. 被引量：7
2Wang Xinghua.On the zeros of analytic functions. J. of Nature . 1981
3Wang Xinghua,Zheng Shiming and Han Danfu.Convergence on Euler’s series, the iterations of Euler’s and Halley’s families. Acta Mathematics Sinica . 1990
4Wang Xinghua.A summary on continuous complexity theory. Contemporary Mathematics . 1994
5Tarski,A.,Givant,S. R.,McKenzie,R. N. A Decision Method for Elementary Algebra and Geometry . 1951
6X. Wang.Convergence of an iterative procedure (in Chinese). Chinese Science Bulletin . 1975
7Smale,S.Newton’’s method estimates from data at one point. The Merging of Disciplines: New Directions in Pure, Applied and Computational Mathematics . 1986
8Kantorovich, L V,Akilov, G. P.Functional Analysis. . 1986

共引文献6

1Xiubin Xu,Chong Li.CONVERGENCE OF NEWTON＇S METHOD FOR SYSTEMS OF EQUATIONS WITH CONSTANT RANK DERIVATIVES[J].Journal of Computational Mathematics,2007,25(6):705-718.
2WANG Xinghua & LI ChongDepartment of Mathematics, Zhejiang University, Hangzhou 310028, China,Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing 100080, China,Department of Applied Mathematics, Southeast University, Nanjing 210096, China.Local and global behavior for algorithms of solving equations[J].Chinese Science Bulletin,2001,46(6):441-448. 被引量：10
3谢治州.关于Newton法的Kantorovich型定理及其优函数[J].数学进展,2012,41(6):641-654.
4魏婷婷,沈卫平,Wei Tingting,Shen Weiping.求解逆特征值问题的牛顿类方法的收敛判据[J].高等学校计算数学学报,2015,37(4):312-325.
5HUANG Zhengda ZHENG Shiming (Department of Mathematics, Xixi Campus, Zhejiang University, Hangzhou 310028, China).ON THE INVARIANT FOR A FAMILY OF DEFORMED HALLEY METHODS[J].Journal of Systems Science & Complexity,2003,16(1):133-144.
6张镇,倪伟才.弱条件下牛顿迭代的收敛性[J].浙江大学学报（理学版）,2003,30(5):503-505. 被引量：5

同被引文献61

1王兴华,韩丹夫.Extraneous fixed points of Euler iteration and corresponding Sullivan's basin[J].Science China Mathematics,2001,44(3):292-298. 被引量：2
2X. D. Li1) , X. D. Sun1) , L. X. Ding2) , Y. M . Wang2) , J. B. Li2) , H. Q. Ru1) and Z. M. Xiu1)1) School of Materials and Metallurgy , Northeastern University , Shenyang 110006 , China2) Department of Materials , School of M.PREPARATION OF YAG ULT RA-FINE POWDER BY CO- PRECIPITATION METHOD[J].Acta Metallurgica Sinica(English Letters),1999,12(5):1184-1187. 被引量：16
3金杰,张安阳.快速成型技术及其应用[J].浙江工业大学学报,2005,33(5):592-595. 被引量：24
4龙爱芳.避免二阶导数计算的迭代法[J].浙江工业大学学报,2005,33(5):602-604. 被引量：2
5刘静,韩丹夫.一族二阶导数计值迭代方法的收敛性[J].浙江大学学报（理学版）,2006,33(1):28-31. 被引量：1
6陈新一.NEWTON迭代法的一个改进[J].数学的实践与认识,2006,36(2):291-294. 被引量：10
7王兴华,韩丹夫.弱条件下的α判据和Newton法[J].计算数学,1997,19(1):103-112. 被引量：18
8李庆扬.数值分析[M].武汉:华中工学院出版社,1986.216-217.
9张德荣.计算方法与算法语言[M].北京：高等教育出版社,1981..
10王兴华,韩丹夫.两族选代的不动点和Julia集[J].计算数学,1997,19(2):219-224. 被引量：5

引证文献19

1王何宇,李冲,王兴华.On relationship between convergence ball of Euler iteration in Banach spaces and its dynamical behavior on Riemann spheres[J].Science China Mathematics,2003,46(3):376-382.
2龙爱芳.避免二阶导数计算的迭代法[J].浙江工业大学学报,2005,33(5):602-604. 被引量：2
3赵岳清.γ-条件下Chebyshev迭代的收敛性[J].内蒙古师范大学学报（自然科学汉文版）,2006,35(1):39-43.
4林荣斐,赵岳清.Banach空间中Jarratt迭代收敛性的注[J].内蒙古师范大学学报（自然科学汉文版）,2006,35(4):413-418.
5葛华丰.一族变型Halley迭代方法的收敛性[J].浙江师范大学学报（自然科学版）,2007,30(2):152-157.
6张新东,王秋华.避免二阶导数计算的Newton迭代法的一个改进[J].山东大学学报（理学版）,2007,42(7):72-76. 被引量：2
7赵岳清.γ-条件下的一个变形牛顿法的收敛性[J].内蒙古师范大学学报（自然科学汉文版）,2007,36(5):558-563.
8Dan-fu Han (Department of Mathematics, Zhejiang University, Hangzhou 310028, China).THE CONVERGENCE ON A FAMILY OF ITERATIONS WITH CUBIC ORDER[J].Journal of Computational Mathematics,2001,19(5):467-474. 被引量：8
9WANG Xinghua & LI ChongDepartment of Mathematics, Zhejiang University, Hangzhou 310028, China,Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing 100080, China,Department of Applied Mathematics, Southeast University, Nanjing 210096, China.Local and global behavior for algorithms of solving equations[J].Chinese Science Bulletin,2001,46(6):441-448. 被引量：10
10王兴华.Convergence of iterations of Euler family under weak condition[J].Science China Mathematics,2000,43(9):958-962. 被引量：5

二级引证文献42

1王何宇,李冲,王兴华.On relationship between convergence ball of Euler iteration in Banach spaces and its dynamical behavior on Riemann spheres[J].Science China Mathematics,2003,46(3):376-382.
2李阳.一般条件下牛顿下降法的收敛性[J].辽宁石油化工大学学报,2004,24(4):90-92.
3李阳.利用优序列方法证明牛顿下降法在一般条件下的收敛性[J].锦州师范学院学报（自然科学版）,2004,25(4):342-345.
4罗先发,叶新涛.一阶Hlder条件下带参数的修正型Euler-Halley迭代族的局部收敛性[J].高等学校计算数学学报,2005,27(2):185-192. 被引量：1
5李阳.牛顿下降法收敛性的一种新证明[J].江西师范大学学报（自然科学版）,2005,29(4):294-297.
6叶新涛,李冲.一阶导数条件下带参数的修正型Euler-Halley迭代族的收敛性[J].数学学报（中文版）,2005,48(5):901-908.
7Guo Xueping.CONVERGENCE BALL OF ITERATIONS WITH ONE PARAMETER[J].Applied Mathematics(A Journal of Chinese Universities),2005,20(4):462-468. 被引量：1
8刘静.γ-条件下变形Chebyshev迭代方法的收敛性及其应用[J].数学的实践与认识,2006,36(10):111-118.
9Xueping Guo.ON SEMILOCAL CONVERGENCE OF INEXACT NEWTON METHODS[J].Journal of Computational Mathematics,2007,25(2):231-242. 被引量：7
10张新东,王秋华.避免二阶导数计算的Newton迭代法的一个改进[J].山东大学学报（理学版）,2007,42(7):72-76. 被引量：2

1王兴华.Convergence of iterations of Euler family under weak condition[J].Science China Mathematics,2000,43(9):958-962. 被引量：5
2胡国恩.ON THE COMMUTATORS OF SINGULAR INTEGRAL OPERATORS[J].Acta Mathematica Scientia,2005,25(3):545-554. 被引量：1
3Guo Qiang PENG.A Weighted Weak Type Endpoint Estimate for the Multilinear Calderón-Zygmund Operators and Its Applications[J].Journal of Mathematical Research and Exposition,2010,30(2):329-337.
4Antonio BOCCUTO,Xenofon DIMITRIOU.Modular Filter Convergence Theorems for Urysohn Integral Operators and Applications[J].Acta Mathematica Sinica,English Series,2013,29(6):1055-1066. 被引量：1
5LIANG Ke-wei,HAN Dan-fu,ZHANG Hong,ZHU Cheng-yan.A weak condition for secant method to solve systems of nonlinear equations[J].Applied Mathematics(A Journal of Chinese Universities),2009,24(1):90-96.
6刘宁,叶永刚.WEAK ORLICZ SPACE AND ITS CONVERGENCE THEOREMS[J].Acta Mathematica Scientia,2010,30(5):1492-1500. 被引量：3
7Marek BALCERZAK,Kazimierz MUSIAL.Vitali Type Convergence Theorems for Banach Space Valued Integrals[J].Acta Mathematica Sinica,English Series,2013,29(11):2027-2036.
8Fang Ainong, Department of Mathematics, Shanghai Jiao Tong University, Shanghai 200030, China.The ACL Property of Homeomorphisms under Weak Conditions[J].Acta Mathematica Sinica,English Series,1998,14(4):473-480.
9Li Juan ZHANG,Hui TONG.Convergence Theorems of Common Elements for Equilibrium Problems and Fixed Point Problems[J].Acta Mathematica Sinica,English Series,2012,28(3):631-636.
10张培璇.ON CONJUGATE QUASI-FOURIER-LEGENDRE-SERIES AND EQUICONVERGENCE THEOREMS[J].Analysis in Theory and Applications,1992,8(4):66-78.

Chinese Science Bulletin

1997年第7期

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