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ON HERMITIAN POSITIVE DEFINITE SOLUTION OF NONLINEAR MATRIX EQUATION X + A* X⁻² A = Q
Journal of Computational Mathematics
Vol. 23, No. 5 (SEPTEMBER 2005), pp. 513-526
Stable URL: http://www.jstor.org/stable/43693260
Page Count: 14
You can always find the topics here!Topics: Matrix equations, Matrices, Linear algebra, Nonlinear equations, Mathematical theorems, Uniqueness, Eigenvalues, Integers, Essential properties
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Based on the fixed-point theory, we study the existence and the uniqueness of the maximal Hermitian positive definite solution of the nonlinear matrix equation X + A* X⁻² A = Q, where Q is a square Hermitian positive definite matrix and A* is the conjugate transpose of the matrix A. We also demonstrate some essential properties and analyze the sensitivity of this solution. In addition, we derive computable error bounds about the approximations to the maximal Hermitian positive definite solution of the nonlinear matrix equation X + A* X⁻² A = Q. At last, we further generalize these results to the nonlinear matrix equation X + A* X-n A = Q, where n ≥ 2 is a given positive integer.
Journal of Computational Mathematics © 2005 Institute of Computational Mathematics and Scientific/Engineering Computing