지원사업
학술연구/단체지원/교육 등 연구자 활동을 지속하도록 DBpia가 지원하고 있어요.
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연구자들이 자신의 연구와 전문성을 널리 알리고, 새로운 협력의 기회를 만들 수 있는 네트워킹 공간이에요.
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We consider the iterative solution of a quadratic matrix equation with special coefficient matrices which arises in the quasibirth and death problem. In this paper, we show that the elementwise minimal positive solvent of the quadratic matrix equations can be obtained using Newton's method if there exists a positive solvent and the convergence rate of the Newton iteration is quadratic if the Fr$\acute{e}$chet derivative at the elementwise minimal positive solvent is nonsingular. Although the Fr$\acute{e}$chet derivative is singular, the convergence rate is at least linear. Numerical experiments of the convergence rate are given.
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참고문헌 (17)
참고문헌 신청
Dario A. Bini / 2005 / Numerical methods for structured Markov chains / Oxford University Press
B.J. Broxson / 2006 / The Kronecker product
Chun-Hua Guo / 2007 / Iterative solution of a nonsymmetric algebraic RICCATI equation / SIAM Journal on Matrix Analysis and Applications 29:396~412
Chun-Hua Guo / 1998 / Analysis and modi cation of newton's method for algebraic RICCATI equations / Mathematics of Computation 67(223):1089~1105
S. Hautphenne / 2008 / Newton's iteration for the extinction probability of a Markovian binary tree / Linear Algebra and its Applications 428:2791~2804
B.J. Broxson / 2006 / The Kronecker product
Chun-Hua Guo / 2007 / Iterative solution of a nonsymmetric algebraic RICCATI equation / SIAM Journal on Matrix Analysis and Applications 29:396~412
Chun-Hua Guo / 1998 / Analysis and modi cation of newton's method for algebraic RICCATI equations / Mathematics of Computation 67(223):1089~1105
S. Hautphenne / 2008 / Newton's iteration for the extinction probability of a Markovian binary tree / Linear Algebra and its Applications 428:2791~2804
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