Solution of a class of nonlinear matrix equations
In this paper we solve nonlinear matrix equations of the formXδ=Q+∑i=1p(Ai⁎Fi(X)Ai)ri andXδ=Q+∑i=1p(Ai⁎Fi(X)Ai)ri+∑j=1q(Bj⁎Gj(X)Bj)qj, where δ∈(−∞,−1]∪[1,∞), ri,qj∈[−1,1], Q∈P(n), the collection of all n×n Hermitian positive definite matrices and Ai,Bj's are n×n matrices, also Fi,Gj's are...
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Veröffentlicht in: | Linear algebra and its applications 2017-10, Vol.530, p.109-126 |
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Sprache: | eng |
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Zusammenfassung: | In this paper we solve nonlinear matrix equations of the formXδ=Q+∑i=1p(Ai⁎Fi(X)Ai)ri andXδ=Q+∑i=1p(Ai⁎Fi(X)Ai)ri+∑j=1q(Bj⁎Gj(X)Bj)qj, where δ∈(−∞,−1]∪[1,∞), ri,qj∈[−1,1], Q∈P(n), the collection of all n×n Hermitian positive definite matrices and Ai,Bj's are n×n matrices, also Fi,Gj's are monotone mappings from P(n) into P(n). Examples are given to illustrate that the equations can not be solved by previously known theorems. |
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ISSN: | 0024-3795 1873-1856 |
DOI: | 10.1016/j.laa.2017.05.006 |