Dissertation > Excellent graduate degree dissertation topics show

pH (?) lder continuous equations inexact Newton method and its convergence

Author: SunHui
Tutor: ZhuDeTong
School: Shanghai Normal University
Course: Operational Research and Cybernetics
Keywords: Inexact Newton method Affine inexact Newton method Recurrence relation R converges Semi-local convergence
CLC: O175
Type: Master's thesis
Year: 2010
Downloads: 15
Quote: 0
Read: Download Dissertation

Abstract


This paper analyzes when an order is Frechet differentiable operator when p-Holder continuous convergence of inexact Newton method , also confirmed through inexact Newton method for solving equations F (x) = 0 the solution x * of the existence of regional reconciliation uniqueness. Furthermore, given the inexact Newton iteration when R in Holder continuous convergence rate . Inexact Newton method is the most commonly used methods of optimization , Dembo, Eisenstat and Steihang in [ 2 ] first proposed inexact Newton method . The authors [ 2 ] studied the inexact Newton method in the local convergence behavior . On the assumption that second-order nonlinear operator continuous Frechet derivative of y satisfy the conditions of deformation of an order of a premise , has been to make the method convergence and superlinear convergence results and corresponding error estimates. Inexact Newton method instead of weaker conditions in addition to the existing method of exact Newton stronger conditions , but also to obtain estimates of the radius of convergence domain . Hernandez in [ 6 ] by constructing two auxiliary functions when an order is given Frechet differentiable operator is Holder continuous Newton's method is accurate semi-local convergence. Author uses two helper functions to establish a precise Newton's method associated with the iterative sequence, by proving that this iteration sequence is a Cauchy sequence to prove the convergence of Newton's method accurately . Meanwhile proved accurate Newton method for solving equations F (x) = 0 the existence of the resulting solution x * of regional reconciliation unique. Furthermore, given the exact Newton Holder continuous when R convergence. This paper will draw on their thoughts, through the introduction of two auxiliary functions prove p-Holder continuous equations inexact Newton method , affine inexact Newton methods and their convergence.

Related Dissertations

  1. Microwave imaging technology and its inexact Newton algorithm,TN015
  2. Nonlinear Programming JFNK homotopy method,O221.2
  3. Numerical Methods for Stochastic Algebraic Riccati Equation,O241
  4. An Inexact Newton Iterative Methods for Solving Large Sparse Nonlinear Equation Systems,O241.6
  5. The Inexact Newton Method for Solving Equality Constrained Optimization Problem,O242.23
  6. Inexact Newton Method for Solving Large Symmetric Sparse Eigenvalue Problems,O241.6
  7. The Technique of Preconditioning and Acceleration for Solving Large Symmetric Sparse Eigenvalue Problems,O241.6
  8. On Inverse Toeplitz Eigenvalue Problem,O241.6
  9. Semi- smooth Newton equations class method,O224
  10. Inexact Methods for Nonlinear Equations and Inverse Eigenvalue Problems,O241.7
  11. Some Theories about Iterative Methods for Solving Nonlinear Equations,O241.6
  12. Application of automatic differentiation inexact Newton method and its promotion,O242.23
  13. On the Study of the Embedding Distribution for Several Classes of Graphs,O157.5
  14. Suspended platform PMLSM Second Order Sliding Mode Control,TP273
  15. Cultural convergence in the choice and beyond,I313
  16. Well-Posedness of Vector Optimization Problems,O224
  17. Some Investigations on Solving Nonlinear Equation,O241.5
  18. The Convergence Analysis of Some High-Order Iterative Methods for Solving Nonlinear Equations,O241.7
  19. Inexact Newton-like Method and Its Application,O242.2
  20. The Study on Modern Optimization Algorithms and Their Applications in the Bilevel Nonlinear Programming,O221.2

CLC: > Mathematical sciences and chemical > Mathematics > Mathematical Analysis > Differential equations, integral equations
© 2012 www.DissertationTopic.Net  Mobile