Generalized α-diagonal dominance
نویسندگان
چکیده
منابع مشابه
Benefits from generalized diagonal dominance
Generalized diagonal dominance, a specific property of the matrix, can be very useful in various fields of the applied linear algebra, as a tool for discovering and proving new results. First, it gives possibility to be able to define different subclasses of H-matrices (papers [3], [11]). Second, it suggests a way to deduce and prove new theorems on the eigenvalue localization (papers [2], [4],...
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Systems of linear differential equations with constant coefficients, as well as Lotka–Volterra equations, with delays in the off–diagonal terms are considered. Such systems are shown to be asymptotically stable for any choice of delays if and only if the matrix has a negative weakly dominant diagonal.
متن کاملDiagonal Dominance and Harmless O -Diagonal Delays1
Systems of linear diierential equations with constant coeecients, as well as Lotka{Volterra equations, with delays in the oo{diagonal terms are considered. Such systems are shown to be asymptotically stable for any choice of delays if and only if the matrix has a negative weakly dominant diagonal.
متن کاملDiagonal Dominance and Positive
We dedicate this paper to Professor Ron Mitchell who has been an inspiration to many generations of numerical analysts. In addition his generous spirit has infused our discipline with a sense of positive endeavour. We examine whether three diierent upwind schemes for the positive definite advection diiusion problem can yield indeenite coeecient matrices. In particular, in line with the increasi...
متن کاملGeneralizations of Diagonal Dominance in Matrix Theory
A matrix A ∈ C is called generalized diagonally dominant or, more commonly, an H−matrix if there is a positive vector x = (x1, · · · , xn) such that |aii|xi > ∑ j 6=i |aij|xj, i = 1, 2, · · · , n. In this thesis, we first give an efficient iterative algorithm to calculate the vector x for a given H-matrix, and show that this algorithm can be used effectively as a criterion for H-matrices. When ...
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ژورنال
عنوان ژورنال: Computers & Mathematics with Applications
سال: 2003
ISSN: 0898-1221
DOI: 10.1016/s0898-1221(03)00150-0