Positive definite solution of two kinds of nonlinear matrix equations
Journal Title: Surveys in Mathematics and its Applications - Year 2009, Vol 4, Issue 0
Abstract
Based on the elegant properties of the Thompson metric, we prove that the following two kinds of nonlinear matrix equations X=<I>Σ<SUB>i=1</SUB><SUP>m</SUP></I> A<SUB>i</SUB><SUP>*</SUP> X<SUP>δ<SUB>i</SUB></SUP>A<SUB>i</SUB> and X=<I>Σ<SUB>i=1</SUB><SUP>m</SUP></I> (A<SUB>i</SUB><SUP>*</SUP> XA<SUB>i</SUB>)<SUP>δ<SUB>i</SUB></SUP>, (0<|δ<SUB>i</SUB>|<1) always have a unique positive definite solution.Iterative methods are proposed to compute the unique positive definite solution. We show that the iterative methods are more effective as δ=max{|δ<SUB>i</SUB>|, i=1,2, ..., m} decreases. Perturbation bounds for the unique positive definite solution are derived in the end.
Authors and Affiliations
Xuefeng Duan, Zhenyun Peng
Keywords
Related Articles
- EP ID EP134371
- DOI -
- Views 91
- Downloads 0
Fonctions et intégrales elliptiques
Identifiability of the multivariate normal by the maximum and the minimum
In this paper, we have discussed theoretical problems in statistics on identification of parameters of a non-singular multi-variate normal when only either the distribution of the maximum or the distribution of the minim...
Multiple periodic solutions for a fourth-order discrete Hamiltonian system
By means of a three critical points theorem proposed by Brezis and Nirenberg and a general version of Mountain Pass Theorem, we obtain some multiplicity results for periodic solutions of a fourth-order discrete Hamiltoni...
A unique common fixed point theorem for occasionally weakly compatible maps
The aim of this paper is to establish a unique common fixed point theorem for two pairs of occasionally weakly compatible single and multi-valued maps in a metric space. This result improves the result of Türkoglu et al....
A survey on dilations of projective isometric representations
In this paper we present Laca-Raeburn's dilation theory of projective isometric representations of a semigroup to projective isometric representations of a group [M.Laca and I.Raeburn, Proc. Amer. Math. Soc., 1995] and M...