期刊文献+
任意字段
题名或关键词
题名
关键词
文摘
作者
第一作者
机构
刊名
分类号
参考文献
作者简介
基金资助
栏目信息

Matrix Completions and Chordal Graphs

Matrix Completions and Chordal Graphs
原文传递
导出
摘要 In a matrix-completion problem the aim is to specify the missing entries of a matrix in order to produce a matrix with particular properties. In this paper we survey results concerning matrix-completion problems where we look for completions of various types for partial matrices supported on a given pattern. We see that the existence of completions of the required type often depends on the chordal properties of graphs associated with the pattern. In a matrix-completion problem the aim is to specify the missing entries of a matrix in order to produce a matrix with particular properties. In this paper we survey results concerning matrix-completion problems where we look for completions of various types for partial matrices supported on a given pattern. We see that the existence of completions of the required type often depends on the chordal properties of graphs associated with the pattern.
作者 KennethJohnHARRISON
机构地区 MurdochUniversity
出处 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2003年第3期577-590,共14页 数学学报（英文版）
关键词 Matrix completions Chordal graph Matrix completions Chordal graph
分类号 O151.21 [理学—基础数学]
  • 相关文献

参考文献26

  • 1Arveson, W. G.: Interpolation problems in nest algebras. J. Funct. Anal., 3, 208-233 (1975).
  • 2Power, S. C.: The distance to the upper triangular operators. Math. Proc. Camb. Phil. Soc., 88, 327-329(1980).
  • 3Parrott, S. K.: On a quotient norm and the Sz.-Nagy Foias lifting theorem. J. Funct. Anal., 30, 311-328(1978).
  • 4Davis, C., Kahan, W. M., Weinberger, W. F.: Norm preserving dilations and the applications to optimal error bounds. SIAM J. Numer. Anal., 19 445-469 (1982).
  • 5Johnson, Charles R., Rodman, Leiba: Completion of partial matrices to contractions. J. Funct. Anal.,69(2), 260-267 (1986).
  • 6Kalman, R. E.: On partial realizations, transfer functions and canonical forms. Acta Polyt. Scand. Math.Comp. Sci Series, MA, 31, 9-31 (1979).
  • 7Kaashoek, M. A., Woerdeman, H. J.: Unique minumal rank extensions of triangular operators. J. Math.Anal. Appl., 131,501-516 (1988).
  • 8Woerdeman, H. J.: The lower order of lower triangular operators and minimal rank extensions. Integral Equations and Operator Theory, 10, 859-879 (1987).
  • 9Furth, D., Sierksma, G.: The rank and eigenvalues of main diagonal perturbed matrices. Report 87-07-OR,Econometrisch Instituut, R. U. Groningen, The Netherlands (1987).
  • 10Cohen, N., Johnson, C. R., Rodman. L, Woerdeman, H .J.: Ranks of completions of partial matrices.Operator Theory, Advances and Appl., 40, 169-185 (1989).
Acta Mathematica Sinica,English Series
2003年 第3期

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