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割线法在Mysovskii型条件下的半局部收敛性定理 被引量：1

Semilocal Convergence Theorem for the Secant Method under Mysovskii-type Condition
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摘要 本文研究求解Banach空间中非线性算子方程的割线法在Mysovskii型条件下的半局部收敛性问题,在一阶差商Hlder连续和逆有界的假设下,建立了相应的收敛性定理,给出了误差估计,最后用数值例子说明所得结果的应用。 The Mysovskii-type condition is considered in this study for the secant method in Banach spaces for solving a nonlinear operator equation. It is assumed that the divided difference of order one is Holder continuous and its inverse is bounded. A semilocal convergence theorem is established, and a error estimate formula is given. Finally, an example is provided to show the application of our theorem.
作者 吴庆标 任红民
机构地区 浙江大学数学系 杭州广播电视大学信息工程学院
出处 《工程数学学报》 CSCD 北大核心 2008年第1期165-168,共4页 Chinese Journal of Engineering Mathematics
基金 浙江省自然科学基金(Y606154)
关键词 割线法 BANACH空间 Mysovskii型条件 半局部收敛性 HSlder连续差商 The secant method Banach space Mysovskii-type condition Semilocal convergence HSlder continuous divided difference
分类号 O241.6 [理学—计算数学]
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参考文献8

  • 1Schmidt J W. Regula-falsi verfahren mit konsistenter steigung und majoranten pinzip[J]. Periodica Mathmematica Hungarica, 1974, 5:187-193.
  • 2王兴华.几个数值求根方法的误差估计[J].数学学报,1979,22(5):638-642.
  • 3Argyros I K. On the secant method[J]. Publicationes Mathematicae Debrecen, 1993, 43:223-238.
  • 4Hernandez M A, Rubion M J. The secant method and divided differences HSlder continuous[J]. Applied Mathematics and Computation, 2001, 15:139-149.
  • 5Hernandez M A, Rubio M J. The secant method for nondifferentiable operators[J]. Applied Mathematics Letters, 2002, 15:395-399.
  • 6Mysovskii I. On the convergence of L.V.Kantorovich's method of solution of functional equations and its application (in Russian)[J]. Dokl Akad Nauk SSSR, 1950, 70:565-568.
  • 7王兴华.关于牛顿法的梅索夫斯基赫定理.数学年刊：A辑,1980,1:228-236.
  • 8Argyros I K. The super-Halley method using divided differences[J]. Applied Mathematics Letters, 1997, 4: 91-95.

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同被引文献12

  • 1Byers R,He C,Mehrmann V.The matrix sign function method and the computation of invariant sub-spaces[J].SIAM Journal on Matrix Analysis and Applications,1997,18(3):615-632.
  • 2Howland J L.The sign matrix and the separation of matrix eigenvalues[J].Linear Algebra and its Appli-cations,1983,49:221-232.
  • 3Bai Z,Demmel J.Using the matrix sign function to compute invariant subspaces[J].SIAM Journal on Matrix Analysis and Applications,1998,19:205-225.
  • 4Benner P,Quintana-Ort′E S.Solving stable generalized Lyapunov equations with the matrix sign func-tion[J].Numerical Algorithms,1999,20(1):75-100.
  • 5Kenney C S,Laub A J,Papadopoulos P M.Matrix-sign algorithms for Riccati equations[J].IMA Journal of Mathematical Control and Information,1992,9:331-344.
  • 6Lancaster P,Rodman L.The Algebraic Riccati Equation[M].Oxford:Oxford University Press,1995.
  • 7Larin V B,Aliev F A.Generalized Lyapunov equation and factorization of matrix polynomials[J].Systems and Control Letters,1993,21(6):485-491.
  • 8Beavers A N,Denman E D.A computational method for eigenvalues and eigenvectors of a matrix with real eigenvalues[J].Numerishe Mathematik,1973,21:389-396.
  • 9Denman E D,Beavers A N.The matrix sign function and computations in systems[J].Applied Mathematics and Computation,1976,2:63-94.
  • 10Kenney C S,Laub A J.Rational iteration methods for the matrix sign function[J].SIAM Journal on Matrix Analysis and Applications,1991,12(2):273-291.

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工程数学学报
2008年 第1期

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