Complex symmetric stabilizing solution of the matrix equation X + A>X−1A = Q

The Matrix Equation X+ATX-1A=Q and Its Application in Nano Research

The matrix equation X + ATX−1A = Q has been studied extensively when A and Q are real square matrices and Q is symmetric positive definite. The equation has positive definite solutions under suitable conditions, and in that case the solution of interest is the maximal positive definite solution. The same matrix equation plays an important role in Green’s function calculations in nano research, ...

Iterative Method for Mirror-Symmetric Solution of Matrix Equation AXB + CY D = E

Iterative algorithm for the generalized ‎$‎(P‎,‎Q)‎$‎-reflexive solution of a‎ ‎quaternion matrix equation with ‎$‎j‎$‎-conjugate of the unknowns

In the present paper‎, ‎we propose an iterative algorithm for‎ ‎solving the generalized $(P,Q)$-reflexive solution of the quaternion matrix‎ ‎equation $overset{u}{underset{l=1}{sum}}A_{l}XB_{l}+overset{v} ‎{underset{s=1}{sum}}C_{s}widetilde{X}D_{s}=F$‎. ‎By this iterative algorithm‎, ‎the solvability of the problem can be determined automatically‎. ‎When the‎ ‎matrix equation is consistent over...

An Improved Structure- Preserving Doubling Algorithm For a Structured Palindromic Quadratic Eigenvalue Problem

In this paper, we present a numerical method to solve the palindromic quadratic eigenvalue problem (PQEP) (λA+λQ+A)z = 0 arising from the vibration analysis of high speed trains, where A, Q ∈ Cn×n have special structures: both Q and A are m × m block matrices with each block being k × k, and moreover they are complex symmetric, block tridiagonal and block Toeplitz, and also A has only one nonze...

On a Nonlinear Matrix Equation Arising in Nano Research

The matrix equation X + AXA = 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 st...