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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.14 No.2
- 발행연도
- 2010.6
- 수록면
- 113 - 124 (12page)
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초록· 키워드
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We consider matrix polynomial which has the form
P₁(X) = A?X<SUP>m </SUP>+ A₁X<SUP>m-1</SUP> + ··· + A<SUB>m</SUB> = 0
where X and A<SUB>i</SUB> are n ￡ n matrices with real elements. In this paper, we propose an iterative method for the symmetric and generalized centro-symmetric solution to the Newton step for solving the equation P₁(X). Then we show that a symmetric and generalized centro-symmetric solvent of the matrix polynomial can be obtained by our Newton’s method. Finally, we give some numerical experiments that confirm the theoretical results.
P₁(X) = A?X<SUP>m </SUP>+ A₁X<SUP>m-1</SUP> + ··· + A<SUB>m</SUB> = 0
where X and A<SUB>i</SUB> are n ￡ n matrices with real elements. In this paper, we propose an iterative method for the symmetric and generalized centro-symmetric solution to the Newton step for solving the equation P₁(X). Then we show that a symmetric and generalized centro-symmetric solvent of the matrix polynomial can be obtained by our Newton’s method. Finally, we give some numerical experiments that confirm the theoretical results.
목차
ABSTRACT
1. INTRODUCTION
2. NEWTON’S METHOD
3. AN ITERATIVE METHOD FOR SOLVING THE EQUATION (2.1)
4. NUMERICAL EXPERIMENTS AND CONCLUSION
5. CONCLUSION
REFERENCES
참고문헌 (20)
참고문헌 신청
1. [학술지(정기간행물)] - Attahiru Sule Alfa / 2003 / Combinded elapsed time and matrix-analytic method for the discrete time GI/G/I and GIX/G/I systems / Qucucing Systems 45 : 5 ~ 25
2. [학술지(정기간행물)] - N. G. Bean / 1997 / The quasi-stationary behavior of quasi-birth-death processes / The Annals of Applied Probability 7 (1) : 134 ~ 155
3. [학술지(정기간행물)] - G. J. Butler / 1985 / Nonnegative solutions of a quadratic matrix equation arising from comparison theorems in ordinary / SIAM J. Alg. Disc. Meth. 6 (1) : 47 ~ 53
4. [학술지(정기간행물)] - H. Dai / 1990 / On the symmetric solutions of linear matrix equations / Linear Algebra and Appl. 131 : 1 ~ 7
5. [학술지(정기간행물)] - George J. Davis / 1981 / Numerical solution of a quadratic matrix equation / SIAM J. Sci. Stat. Comput. 2 (2) : 164 ~ 175
2. [학술지(정기간행물)] - N. G. Bean / 1997 / The quasi-stationary behavior of quasi-birth-death processes / The Annals of Applied Probability 7 (1) : 134 ~ 155
3. [학술지(정기간행물)] - G. J. Butler / 1985 / Nonnegative solutions of a quadratic matrix equation arising from comparison theorems in ordinary / SIAM J. Alg. Disc. Meth. 6 (1) : 47 ~ 53
4. [학술지(정기간행물)] - H. Dai / 1990 / On the symmetric solutions of linear matrix equations / Linear Algebra and Appl. 131 : 1 ~ 7
5. [학술지(정기간행물)] - George J. Davis / 1981 / Numerical solution of a quadratic matrix equation / SIAM J. Sci. Stat. Comput. 2 (2) : 164 ~ 175
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UCI(KEPA) : I410-ECN-0101-2010-410-002410210