Characterization of diagonally dominant H-matrices
نویسندگان
چکیده
منابع مشابه
Doubly Diagonally Dominant Matrices
We consider the class of doubly diagonally dominant matrices (A = [ ajj] E C”, ‘, la,,1 l”jjl > Ck+ i laiklCk+ jlajkl. i #j) and its subclasses. We give necessary and sufficient conditions in terms of the directed graph for an irreducibly doubly diagonally dominant matrix to be a singular matrix or to be an H-matrix. As in the case of diagonal dominance, we show that the Schur complements of do...
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OF DISSERTATION RELATIVE PERTURBATION THEORY FOR DIAGONALLY DOMINANT MATRICES Diagonally dominant matrices arise in many applications. In this work, we exploit the structure of diagonally dominant matrices to provide sharp entrywise relative perturbation bounds. We first generalize the results of Dopico and Koev to provide relative perturbation bounds for the LDU factorization with a well condi...
متن کاملSubdirect sums of doubly diagonally dominant matrices
The problem of when the k-subdirect sum of a doubly diagonally dominant matrix (DDD matrix) is also a DDD matrix is studied. Some sufficient conditions are given. The same situation is analyzed for diagonally dominant matrices and strictly diagonally dominant matrices. Additionally, some conditions are also derived when card(S)>card(S1) which was not studied by Bru, Pedroche and Szyld [Electron...
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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 p...
متن کاملOn Schur complements of doubly diagonally dominant matrices and H-matrices
Given a matrix family, it is interesting to know whether some important properties or structures of the class of matrices are inherited by their submatrices or by the matrices associated with the original matrices. It is known that the principal submatrices and the Schur complements of positive semidefinite matrices are positive semidefinite matrices; the same is true of M-matrices, H-matrices,...
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ژورنال
عنوان ژورنال: Publications de l'Institut Mathematique
سال: 2017
ISSN: 0350-1302,1820-7405
DOI: 10.2298/pim1715065m