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논문 기본 정보
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- 한국산업응용수학회 JOURNAL OF THE KOREAN SOCIETY FOR INDUSTRIAL AND APPLIED MATHEMATICS Journal of the Korean Society for Industrial and Applied Mathematics Vol.11 No.4
- 발행연도
- 2007.12
- 수록면
- 39 - 46 (8page)
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초록· 키워드
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One of well known and much studied nonlinear matrix equations is the matrix polynomial which has the form G(X)=A?X<SUP>m</SUP>+A₁X<SUP>m-1</SUP>+…+A<SUB>m</SUB>, where A?, A₁, …, A<SUB>m</SUB> and X are n×n real matrices. We show how the minimization methods can be used to solve the matrix polynomial G(X) and give some numerical experiments. We also compare Polak and Ribiere version and Fletcher and Reeves version of conjugate gradient method.
목차
Abstract
1. Introduction
2. Conjugate Gradient Methods for Solving a Matrix Polynomial
3. Algorithms for Solving G(X)=0 by Conjugate Gradient Methods
4. Numerical Experiment and Conclusion
References
참고문헌 (8)
참고문헌 신청
, 198 , Numerical solution of a quadratic matrix equation.SIAM J.
, 1983. , An algorithm to compute solvents of the matrix equationAX 2 + BX + C = 0. ACM Trans. Math. Software
, 1964. , R. Fletcher and C. M. Reeves. Function minimization by conjugate gradients.ComputerJ.
, 2000. , Numerical analysis of a quadratic matrix equation 20 (4) : 499 ~ 519
, 2001 , Solving a quadratic matrix equations by Newton'smethod with exact line searches 23 (2) : 303 ~ 316
, 1983. , An algorithm to compute solvents of the matrix equationAX 2 + BX + C = 0. ACM Trans. Math. Software
, 1964. , R. Fletcher and C. M. Reeves. Function minimization by conjugate gradients.ComputerJ.
, 2000. , Numerical analysis of a quadratic matrix equation 20 (4) : 499 ~ 519
, 2001 , Solving a quadratic matrix equations by Newton'smethod with exact line searches 23 (2) : 303 ~ 316
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