An Improvement on Disc Separation of the Schur Complement and Bounds for Determinants of Diagonally Dominant Matrices
نویسندگان
چکیده
In this paper, we improve the disc separation of the Schur complement of strictly diagonally dominant matrices presented in Liu [SIAM. J. Matrix Anal. Appl., 27 (2005): 665-674]. As applications, we present some new bounds for determinants of original matrices and estimations for eigenvalues of Schur complement. By theoretical analysis, we improve the bounds of determinants established in Huang [Comput. Math. Appl., 50 (2005): 1677-1684].
منابع مشابه
Disc Separation of the Schur Complement of Diagonally Dominant Matrices and Determinantal Bounds
We consider the Geršgorin 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 dia...
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The result on the Geršgorin disc separation from the origin for strictly diagonally dominant matrices and their Schur complements in (Liu and Zhang in SIAM J. Matrix Anal. Appl. 27(3):665-674, 2005) is extended to nonstrictly diagonally dominant matrices and their Schur complements, showing that under some conditions the separation of the Schur complement of a nonstrictly diagonally dominant ma...
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As is well known, the Schur complements of strictly or irreducibly diagonally dominant matrices are H−matrices; however, the same is not true of generally diagonally dominant matrices. This paper proposes some conditions on the generally diagonally dominant matrix A and the subset α ⊂ {1, 2, . . . , n} so that the Schur complement matrix A/α is an H−matrix. These conditions are then applied to ...
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As is known, the Schur complements of diagonally dominant matrices are diagonally dominant; the same is true of doubly diagonally dominant matrices. The purpose of this paper is to extend the results to the generalized doubly diagonally dominant matrices (a proper subset of H -matrices); that is, we show that the Schur complement of a generalized doubly diagonally dominant matrix is a generaliz...
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