지원사업
학술연구/단체지원/교육 등 연구자 활동을 지속하도록 DBpia가 지원하고 있어요.
커뮤니티
연구자들이 자신의 연구와 전문성을 널리 알리고, 새로운 협력의 기회를 만들 수 있는 네트워킹 공간이에요.
초록· 키워드
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One of the interesting nonlinear matrix equations is the qua-dratic matrix equation defined by Q(X) = AX2 + BX + C = 0, where X is a n×n unknown real matrix, and A,B and C are n×n givenmatrices with real elements. Another one is the matrix polynomial P(X) = A0Xm + A1Xm−1 + · · · + Am = 0, X,Ai 2 Rn×n.
Newton’s method is used to find the symmetric and bisymmetric solventsof the nonlinear matrix equations Q(X) and P(X). The method does notdepend on the singularity of the Fr´echet derivative. Finally, we give somenumerical examples.
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참고문헌 (12)
참고문헌 신청
C.-H. Guo / 2000 / On the iterative solution of a class of nonsymmetric algebraic equations / SIAM J. Matrix Anal. Appl 22 (2) : 376 ~ 391
D. X. Xie / 2000 / The solvability conditions for the inverse problem of bisymmetric nonnegative definite matrices / J. Comput. Math 6 (6) : 597 ~ 608
G. J. Davis / 1981 / Numerical solution of a quadratic matrix equation / SIAM J. Sci. Statist. Comput 2 (2) : 164 ~ 175
G. J. Davis / 1983 / Algorithm 598: An algorithm to compute solvents of the matrix equation AX2+ BX + C = 0 / ACM Trans. Math. Software 9 (2) : 246 ~ 254
G. M. Phillips / 1996 / Theory and Applications of Numerical Analysis / Aca- demic Press
D. X. Xie / 2000 / The solvability conditions for the inverse problem of bisymmetric nonnegative definite matrices / J. Comput. Math 6 (6) : 597 ~ 608
G. J. Davis / 1981 / Numerical solution of a quadratic matrix equation / SIAM J. Sci. Statist. Comput 2 (2) : 164 ~ 175
G. J. Davis / 1983 / Algorithm 598: An algorithm to compute solvents of the matrix equation AX2+ BX + C = 0 / ACM Trans. Math. Software 9 (2) : 246 ~ 254
G. M. Phillips / 1996 / Theory and Applications of Numerical Analysis / Aca- demic Press
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