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Article
Disc Separation of the Schur Complement of Diagonally Dominant Matrices and Determinantal Bounds
SIAM Journal on Matrix Analysis and Applications
  • Jianzhou Liu, Xiangtan University
  • Fuzhen Zhang, Nova Southeastern University
Document Type
Article
Publication Date
12-1-2005
Keywords
  • Brauer theorem,
  • Comparison matrix,
  • Diagonally dominant matrix,
  • Doubly diagonally dominant matrix,
  • Gersgorin theorem,
  • H-matrix,
  • M-matrix,
  • Schur complement,
  • Separation
Disciplines
Peer Reviewed
1
Abstract
We consider the Gersgorin disc separation from the origin for (doubly) diagonally dominant matrices and their Schur complements, showing that the separation of the Schur complement of a (doubly) diagonally dominant matrix is greater than that of the original grand matrix. As application we discuss the localization of eigenvalues and present some upper and lower bounds for the determinant of diagonally dominant matrices.
Comments

AMS subject classifications. 15A45, 15A48

DOI
10.1137/040620369
Citation Information
Jianzhou Liu and Fuzhen Zhang. "Disc Separation of the Schur Complement of Diagonally Dominant Matrices and Determinantal Bounds" SIAM Journal on Matrix Analysis and Applications Vol. 27 Iss. 3 (2005) p. 665 - 674 ISSN: 0895-4798
Available at: http://works.bepress.com/fuzhen-zhang/34/