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논문 기본 정보
- 자료유형
- 학술저널
- 저자정보
- 발행연도
- 2019.1
- 수록면
- 341 - 349 (9page)
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In this paper, we are concerned with the minimal positive solution to system of the nonlinear matrix equations A1X2+B1Y +C1 = 0 and A2Y 2 +B2X +C2 = 0, where Ai is a positive matrix or a nonnegative irreducible matrix, Ci is a nonnegative matrix and −Bi is a nonsingular M-matrix for i = 1,2. We apply Newton’s method to system and present a modified Newton’s iteration which is validated to be efficient in the numerical experiments. We prove that the sequences generated by the modified Newton’s iteration converge to the minimal positive solution to system of nonlinear matrix equations.
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참고문헌 (12)
참고문헌 신청
D. A. Bini. / 2009 / The cyclic reduction algorithm: from Poisson equation to stochas-tic processes and beyond / Numerical Algorithms 51:23~60
G. J. Davis / 1983 / Algorithm 598: An algorithm to compute solvents of the matrix equation AX2 + BX + C = 0 / ACM Trans. Math. Software 9:246~254
J. E. Dennis & Jr / 1983 / Numerical Methods for Unconstrained Optimiza-tion and Nonlinear Equations / Prentice-Hall
C.-H. Guo / 2007 / Iterative solution of a nonsymmetric algebraic Riccati equa-tion / SIAM J. Matrix Anal. Appl 29:396~412
N.J. Higham / 2006 / Solving a duadratic matrix equation by Newton's method with exact line searches / SIAM J. Matrix. Anal. Appl 23:303~316
G. J. Davis / 1983 / Algorithm 598: An algorithm to compute solvents of the matrix equation AX2 + BX + C = 0 / ACM Trans. Math. Software 9:246~254
J. E. Dennis & Jr / 1983 / Numerical Methods for Unconstrained Optimiza-tion and Nonlinear Equations / Prentice-Hall
C.-H. Guo / 2007 / Iterative solution of a nonsymmetric algebraic Riccati equa-tion / SIAM J. Matrix Anal. Appl 29:396~412
N.J. Higham / 2006 / Solving a duadratic matrix equation by Newton's method with exact line searches / SIAM J. Matrix. Anal. Appl 23:303~316
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