Solution of a class of nonlinear matrix equations
Copyright policy )Solution of a class of nonlinear matrix equations
In this article we present several necessary and sufficient conditions for the existence of Hermitian positive definite solutions of nonlinear matrix equations of the form $X^s + A^*X^{-t}A + B^*X^{-p}B = Q$, where $ s, t, p \geq 1$, $ A, B$ are nonsingular matrices and $Q$ is a Hermitian positive definite matrix. We derive some iterations to compute the solutions followed by some examples. In this context we also discuss about the maximal and the minimal Hermitian positive definite solution of this particular nonlinear matrix equation.
20 pages, 2 figures
- Indian Statistical Institute India
- Aliah University India
- Jadavpur University India
Thompson metric, partially ordered set, Mathematics - Functional Analysis, matrix equation, Fixed-point theorems, fixed point, 15A24, 47H10, 47H09, Matrix equations and identities, FOS: Mathematics, Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc., Functional Analysis (math.FA)
Thompson metric, partially ordered set, Mathematics - Functional Analysis, matrix equation, Fixed-point theorems, fixed point, 15A24, 47H10, 47H09, Matrix equations and identities, FOS: Mathematics, Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc., Functional Analysis (math.FA)
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