Ela the Eigenvalue Distribution of Schur Complements of Nonstrictly Diagonally Dominant Matrices and General H−matrices∗

نویسندگان

  • CHENG-YI ZHANG
  • SHUANGHUA LUO
  • FENGMIN XU
  • CHENGXIAN XU
  • Cheng-yi Zhang
  • Shuanghua Luo
  • Fengmin Xu
  • Chengxian Xu
چکیده

The paper studies the eigenvalue distribution of Schur complements of some special matrices, including nonstrictly diagonally dominant matrices and general H−matrices. Zhang, Xu, and Li [Theorem 4.1, The eigenvalue distribution on Schur complements of H-matrices. Linear Algebra Appl., 422:250–264, 2007] gave a condition for an n×n diagonally dominant matrix A to have |JR+(A)| eigenvalues with positive real part and |JR−(A)| eigenvalues with negative real part, where |JR+(A)| (|JR−(A)|) denotes the number of diagonal entries of A with positive (negative) real part. This condition is applied to establish some results about the eigenvalue distribution for the Schur complements of nonstrictly diagonally dominant matrices and general H−matrices with complex diagonal entries. Several conditions on the n×n matrix A and the subset α ⊆ N = {1, 2, · · · , n} are presented so that the Schur complement A/α of A has |JR+(A)|−|J α R+ (A)| eigenvalues with positive real part and |JR−(A)| − |J α R− (A)| eigenvalues with negative real part, where |J R+(A)| (|J α R− (A)|) denotes the number of diagonal entries of the principal submatrix A(α) of A with positive (negative) real part.

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تاریخ انتشار 2009