Comparison theorems using general cones for norms of iteration matrices
نویسندگان
چکیده
We prove comparison theorems for norms of iteration matrices in splittings of matrices in the setting of proper cones in a finite dimensional real space by considering cone linear absolute norms and cone max norms. Subject to mild additional hypotheses, we show that these comparison theorems can hold only for such norms within the class of cone absolute norms. Finally, in a Banach algebra setting, we prove a comparison theorem for spectral radii without appealing to Perron–Frobenius theory. © 2004 Elsevier Inc. All rights reserved. AMS classification: 15A18; 15A42; 15A48; 15A60
منابع مشابه
Comparison of Convergence of General Stationary Iterative Methods for Singular Matrices
New comparison theorems are presented comparing the asymptotic convergence factor of iterative methods for the solution of consistent (as well as inconsistent) singular systems of linear equations. The asymptotic convergence factor of the iteration matrix T is the quantity γ(T ) = max{|λ|, λ ∈ σ(T ), λ = 1}, where σ(T ) is the spectrum of T . In the new theorems, no restrictions are imposed on ...
متن کاملA full NT-step O(n) infeasible interior-point method for Cartesian P_*(k) –HLCP over symmetric cones using exponential convexity
In this paper, by using the exponential convexity property of a barrier function, we propose an infeasible interior-point method for Cartesian P_*(k) horizontal linear complementarity problem over symmetric cones. The method uses Nesterov and Todd full steps, and we prove that the proposed algorithm is well define. The iteration bound coincides with the currently best iteration bound for the Ca...
متن کاملSome New Comparison Theorems for Double Splittings of Matrices
In this paper, we further investigate the double splitting iterative methods for solving linear systems. Building on the previous work by Song and Song [Convergence for nonnegative double splittings of matrices, Calcolo, (2011) 48: 245-260], some new comparison theorems for the spectral radius of double splittings of matrices under suitable conditions are presented.
متن کاملConvergence theorems of an implicit iteration process for asymptotically pseudocontractive mappings
The purpose of this paper is to study the strong convergence of an implicit iteration process with errors to a common fixed point for a finite family of asymptotically pseudocontractive mappings and nonexpansive mappings in normed linear spaces. The results in this paper improve and extend the corresponding results of Xu and Ori, Zhou and Chang, Sun, Yang and Yu in some aspects.
متن کاملDhage iteration method for PBVPs of nonlinear first order hybrid integro-differential equations
In this paper, author proves the algorithms for the existence as well as the approximation of solutions to a couple of periodic boundary value problems of nonlinear first order ordinary integro-differential equations using operator theoretic techniques in a partially ordered metric space. The main results rely on the Dhage iteration method embodied in the recent hybrid fixed point theorems of D...
متن کامل