Relative Perturbation Theory for Diagonally Dominant Matrices
نویسندگان
چکیده
منابع مشابه
Relative Perturbation Theory for Diagonally Dominant Matrices
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...
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For a symmetric positive semi-definite diagonally dominant matrix, if its off-diagonal entries and its diagonally dominant parts for all rows (which are defined for a row as the diagonal entry subtracted by the sum of absolute values of off-diagonal entries in that row) are known to a certain relative accuracy, we show that its eigenvalues are known to the same relative accuracy. Specifically, ...
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متن کاملDoubly 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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ژورنال
عنوان ژورنال: SIAM Journal on Matrix Analysis and Applications
سال: 2014
ISSN: 0895-4798,1095-7162
DOI: 10.1137/130943613