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On a Nonlinear Matrix Equation Arising in Nano Research

2012
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SIAM Journal on Matrix Analysis and Applications
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The matrix equation X + A X −1 A = Q arises in Green's function calculations in nano research, where A is a real square matrix and Q is a real symmetric matrix dependent on a parameter and is usually indefinite. In practice one is mainly interested in those values of the parameter for which the matrix equation has no stabilizing solutions. The solution of interest in this case is a special weakly stabilizing complex symmetric solution X * , which is the limit of the unique stabilizing solution

doi:10.1137/100814706
fatcat:5wli44ft5vbfbhgiomqr6p666y