Formulas for calculating the extremum ranks and inertias of a four-term quadratic matrix-valued function and their applications
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Publication:426078
DOI10.1016/j.laa.2012.03.021zbMath1252.15026OpenAlexW2094497608MaRDI QIDQ426078
Publication date: 11 June 2012
Published in: Linear Algebra and its Applications (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.laa.2012.03.021
optimizationquadratic formsranklinearization methodinertiaLöwner partial orderingmatrix inequalityquadratic matrix-valued functiongeneralized algebraic Riccati equationcomplex Hermitian matrixquadratic matrix equations
Numerical mathematical programming methods (65K05) Semidefinite programming (90C22) Quadratic programming (90C20) Matrix equations and identities (15A24) Eigenvalues, singular values, and eigenvectors (15A18) Positive matrices and their generalizations; cones of matrices (15B48) Hermitian, skew-Hermitian, and related matrices (15B57) Miscellaneous inequalities involving matrices (15A45) Quadratic and bilinear forms, inner products (15A63) Matrices over function rings in one or more variables (15A54) Vector spaces, linear dependence, rank, lineability (15A03)
Related Items
The optimization on ranks and inertias of a quadratic Hermitian matrix function and its applications ⋮ The extremal ranks and inertias of matrix expressions with respect to generalized reflexive and anti-reflexive matrices with applications ⋮ Some optimization problems on ranks and inertias of matrix-valued functions subject to linear matrix equation restrictions ⋮ Solutions of a constrained Hermitian matrix-valued function optimization problem with applications ⋮ Quadratic properties of least-squares solutions of linear matrix equations with statistical applications ⋮ Extremal ranks of some nonlinear matrix expressions with applications ⋮ Rank/inertia approaches to weighted least-squares solutions of linear matrix equations ⋮ The solutions to the quadratic matrix equation \(X^* A X + B^* X + D = 0\) ⋮ Matrix rank/inertia formulas for least-squares solutions with statistical applications ⋮ An alternative approach for solving the quadratic matrix equation \(C^\ast X^\ast A X C + C^\ast X^\ast B + B^\ast X C + D = 0\)
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