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矩阵方程X+A~*X^(-q)A=Q(q≥1)的Hermitian正定解 被引量：5

HERMITIAN POSITIVE DEFINITE SOLUTIONS OF THE MATRIX EQUATION X+A~*X^(-q)A=Q(q≥1)
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摘要 本文研究矩阵方程X+A~*X^(-q)A=Q(q≥1)的Hermitian正定解,给出了存在正定解的充分条件和必要条件,构造了求解的迭代方法.最后还用数值例子验证了迭代方法的可行性和有效性. The Hermitian positive definite solutions of the matrix equaution X＋A^＊X^-qA=Q（q≥1） is investigated. Some sufficient conditions and necessary conditions for the existence of positive definite solutions are given. An iterative method for computing Hermitian positive definite solutions is proposed. Numerical examples are given to illustrate the performance and the effectiveness of the iterative method.
作者 廖安平 段雪峰 沈金荣
机构地区 长沙学院数学研究所 湖南大学数学与计量经济学院 长沙学院信息与计算科学系
出处 《计算数学》 CSCD 北大核心 2008年第4期369-378,共10页 Mathematica Numerica Sinica
基金 长沙学院科研基金资助(CDJJ-08010104).
关键词 矩阵方程 正定解 迭代方法 Matrix equation, Positive definite solution, Iterative method
分类号 O241.6 [理学—计算数学]
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参考文献25

  • 1Bhatia R. Matrix Analysis, Springer, Berlin, 1997.
  • 2陈小山,黎稳.关于矩阵方程X+A~*X^(-1)A=P的解及其扰动分析[J].计算数学,2005,27(3):303-310. 被引量：19
  • 3Salah M. E1-Sayed and Asmaa M. A1-Dbiban. On positive definite solutions of the nonlinear matrix equation X + A^*X^-nA = I[M]. Appl. Math. Comput., 2004, 151: 533-541.
  • 4Salah M. E1-Sayed and Milko G. Petkov. Iterative methods for nonlinear matrix equation X + A^*X-αA = I(α > 0)[J]. Linear Algebra Appl., 2005, 403: 45-52.
  • 5Jacob C. Engwerda, Andre C. M. Ran and Arie L. Rijkeboer. Necessary and sumcient conditions for the existence of a positive definite solution of the matrix equation X + A^*X^-1A = Q[J]. Linear Algebra Appl., 1993, 186: 255-275.
  • 6Jacob C. Engwerda. On the existence of a positive definite solution of the matrix equation X + A^TX^-1A = I[J]. Linear Algebra Appt., 1993, 194: 91-108.
  • 7Furuta T. Operator inequalities associated with Holder-McCarthy and Kantorovich inequalities[J]. J. Inequal. Appl., 1998, 6: 137-148.
  • 8Chunhua Guo and Peter Lancaster, Iterative solution of two matrix equations[J]. Math. Comput., 1999, 68: 1589-1603.
  • 9Vejdi I. Hasanov. Positive definite solutions of the matrix equations X ± A^*X^-qA = Q(O < q ≤ 1)[J]. Linear Algebra Appl., 2005, 404: 166-182.
  • 10Vejdi I. Hasanov and Salah M. El-Sayed, On positive definite solutions of the nonlinear matrix equation X + A^*X^-bA = Q(O < δ≤ 1)[J]. Linear Algebra Appl., 2006, 412: 154-160.

二级参考文献10

  • 1Anderson W.N., Morley T.D., Trapp G.E., Positive solutions to X = A-BX^-1B*, Linear Algebra Appl., 134(1990), 53-62.
  • 2Engwerda J.C., On the existence of a positive definite solution of the matrix equation X + A^TX^-1A = I, Linear Algebra Appl., 194 C1993), 91-108.
  • 3Engwerda J.C., Ran A.C.M., Rijkeboer A.L., Necessary and sufficient conditions for the existence of a positive definite solution of the matrix equation X + A^*X^-1A = I, Linear Algebra Appl., 186(1993), 255-275.
  • 4Zhan X., On the matrix equation X + A*X-1A = I, Linear Algebra Appl., 247 (1996),337-345.
  • 5Xu S.F., Perturbation analysis of the maximal solution of the matrix equation X +A^*X^-1A = P, Linear Algebra Appl., 336 (2001), 61-70.
  • 6Sun J.G., Xu S.F., Perturbation analysis of the maximal solution of the matrix equation X + A^*X^-1A = P.II, Linear Algebra Appl., 362 (2003), 211-228.
  • 7Liu X.G., Gao H., On the positive definite solutions of the matrix equations X^s±A^T X^-tA = In, Linear Algebra Appl., 368 (2003), 83-97.
  • 8Ran A.C.M., Reurings M.C.B., On the nonlinear matrix equation X + A^*F(X)A = Q:solutions and perturbation theory, Linear Algebra Appl., 346 (2002), 15-26.
  • 9Zhang Yuhai, On Hermitian positive definite solutions of matrix equation X + A^*X^-2A =I, Linear Algebra Appl., 326 (2001), 27-44.
  • 10刘新国.关于求解矩阵方程I=X+A^HX^(-1)A的简单迭代[J].高等学校计算数学学报,1998,20(2):163-167. 被引量：3

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计算数学
2008年 第4期

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