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Minimization Method for Solving a Quadratic Matrix Equation

김현민
경북대학교 자연과학대학 수학과|2007.06|Kyungpook Mathematical Journal|제47권 제2호|pp. 239-251

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참고문헌

키워드

quadratic matrix equationconjugate gradient methodlocal and global minimizers
주제분류수학

초록

We show how the minimization can be used to solve the quadratic matrix equation and then compare two different types of conjugate gradient method which are Polak and Ribiere version and Fletcher and Reeves version. Finally,some results of the global and local convergence are shown.

Abstract

We show how the minimization can be used to solve the quadratic matrix equation and then compare two different types of conjugate gradient method which are Polak and Ribiere version and Fletcher and Reeves version. Finally,some results of the global and local convergence are shown.

참고문헌 (15)

  1. "Descent property and global convergence of the Fletcher-Reeves method with inexact line search", pp.121~124 (1985)
  2. "The solution of the matrix equation AXB �", pp.93~105 (1987)
  3. "H. P. Crowder and P. Wolfe. Linear convergence of the conjugate gradient method IBM Journal of Research and development", pp.431~433 (1972)
  4. "George J. Davis. Numerical solution of a quadratic matrix equation", pp.164~175
  5. "Numerical Methods for Unconstrained Optimization and Nonlinear Equations" (1983), Prentice-Hall
  6. "Function minimization by conjugate gradients", pp.149~154 (1964)
  7. "Practical Methods of Optimization" (1987)
  8. "Elementary Matrices and Some Applications to Dynamics and Di erential Equations", Cambridge University Press
  9. "Numerical analysis of a quadratic matrix equation", 20(4), pp.499~519 (2000)
  10. "Solving a quadratic matrix equation by New- ton's method with exact line searches", 23(2), pp.303~316 (2001)
  11. "Numerical methods for solving a quadratic matrix equation" (2000)
  12. "Conjugate gradient methods and nonlinear optimization In Loyce Adams and J. L. Nazareth, editors, Linear and Nonlinear Conjugate Gradient-Related Methods", pp.9~23 (1996), Society for Industrial and Applied Mathematics
  13. "Numerical Optimization" (1999), Springer-Verlag, New York
  14. "A Fortran subroutine for solving systems of nonlinear algebraic equations Numerical Methods for Nonlinear Algebraic Equations" (1970)
  15. "Lecture Notes in Mathematics" (1984)

관련 논문AI추천

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