期刊文献+

矩阵方程X+sum from i=1 to m (A_i~*XV^(-n)A_i=I)的正定解 被引量:5

下载PDF
导出
摘要 研究了非线性矩阵方程X+sum from i=1 to m (A_i~*XV^(-n)A_i=I)存在正定解的充分和必要条件,得到了正定解的存在区间,给出了存在唯一解的充分条件,构造了求解的迭代方法.
出处 《长沙大学学报》 2009年第2期1-4,共4页 Journal of Changsha University
基金 长沙大学青年基金(批准号:DJJ-08010104)资助项目
  • 相关文献

参考文献7

  • 1Anderson W N, et al. Positive solutions to X = A - BX^-1 B^*[J]. Linear Algebra Appl. , 1990,(134) :53 -62. 被引量:1
  • 2El- sayed S M, et al. On positive definite solutions of the nonlinear matrix equation X + A^* X^-a A = I [ J ]. Appl. Math. Comput. , 2004, 151(2) : 533 -541. 被引量:1
  • 3Ivanov I G, et al. On matrix equations X± A^* X^-2A =I [J]. Linear Algebra Appl , 2001 ,(326) : 27 -44. 被引量:1
  • 4Hassanov V I, et al. Solutions and perturbation estimates for the matrix equations X ± A^* X^-a A = Q [ J ]. Appl. Marh. Comput. , 2004, 156(2) : 513 -525. 被引量:1
  • 5廖安平,段雪峰,沈金荣.矩阵方程X+A~*X^(-q)A=Q(q≥1)的Hermitian正定解[J].计算数学,2008,30(4):369-378. 被引量:6
  • 6Bhatia R. Matrix analusis[M]. Berlin: Springer-Verlag, 1997. 被引量:1
  • 7孙继广著..矩阵扰动分析[M].北京:科学出版社,2001:482.

二级参考文献25

  • 1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
  • 2Bhatia R. Matrix Analysis, Springer, Berlin, 1997. 被引量:1
  • 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. 被引量:1
  • 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. 被引量:1
  • 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. 被引量:1
  • 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. 被引量:1
  • 7Furuta T. Operator inequalities associated with Holder-McCarthy and Kantorovich inequalities[J]. J. Inequal. Appl., 1998, 6: 137-148. 被引量:1
  • 8Chunhua Guo and Peter Lancaster, Iterative solution of two matrix equations[J]. Math. Comput., 1999, 68: 1589-1603. 被引量:1
  • 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. 被引量:1
  • 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. 被引量:1

共引文献5

同被引文献27

  • 1Anderson W N, Morley T D, Trapp G E. Positive solutions to X — A~ BX~1B* [J]. Linear Algebra Appl., 1990, 134: 53-62. 被引量:1
  • 2Engwerda J C. On the existence of the positive definite solution of the matrix equation X + ATX~lA — /[J]. Linear Algebra Appl., 1993,194: 91-108. 被引量:1
  • 3Vejdi I Hassanov. Positive definite solutions of the matrix equations X 土 A*X~qA — Q*[J]. Linear Algebra Appl., 2005, 404: 166-182. 被引量:1
  • 4Wang Xingtao, Li Yuanming. On equations that are equivalent to the nonlinear matrix equation X + A*X~aA = Q[J]. J. Comput. Appl. Math., 2010, 234: 2441-2449. 被引量:1
  • 5Long Jianhui, Hu Xiyan, Zhang Lei. On the Hermitian positive definite solution of the nonlinear matrix equation X + A*X~xA + B*X~xB = /[J]. Bull Braz. Math. Soc. New. Series, 2008, 39(3): 371-386. 被引量:1
  • 6He Youmei, Long Jianhui. On the Hermitian positive definite solution of the nonlinear matrixequation X + 々Hi = /[J]. Appl. Math. Comput., 2010, 216: 3480-3485. 被引量:1
  • 7Sarhan A M, Naglaa M El-Shazly, Enas M Shehata. On the existence of extremal positive definitemsolutions of the nonlinear matrix equationXr + A*XSiAi ~ /[J], Math. Computer Modelling, 2010, 51: 1107-1117. 被引量:1
  • 8Duan Xuefeng, Liao Anping, Tang Bin. On the nonlinear matrix equation X ~— Q[Jj-j_ iLinear Algebra Appl. , 2008, 429: 110-121. 被引量:1
  • 9Duan Xuefeng, Liao Anping. On Hermitian positive definite solution of the matrix equation X —A*XrAi — Q[J]. Journal of Computational and Applied Mathematics, 2009, 229: 27-36. 被引量:1
  • 10Parodi M. La localisation des valeurs caracterisiques des matrices et ses application[M]. Paris: Gau-thiervillars, 1959. 被引量:1

引证文献5

二级引证文献3

相关作者

内容加载中请稍等...

相关机构

内容加载中请稍等...

相关主题

内容加载中请稍等...

浏览历史

内容加载中请稍等...
;
使用帮助 返回顶部