Necessary and sufficient conditions for the existence of a Hermitian positive definite solution of a type of nonlinear matrix equations.
Negative powers and the spectrum of matrices
New estimates for the solution of the Lyapunov matrix differential equation.
New lower solution bounds for the continuous algebraic Riccati equation.
New SOR-like methods for solving the Sylvester equation
We present new iterative methods for solving the Sylvester equation belonging to the class of SOR-like methods, based on the SOR (Successive Over-Relaxation) method for solving linear systems. We discuss convergence characteristics of the methods. Numerical experimentation results are included, illustrating the theoretical results and some other noteworthy properties of the Methods.
New trace bounds for the product of two matrices and their applications in the algebraic Riccati equation.
Nonrecursive solution for the discrete algebraic Riccati equation and X + A*X -1 A=L
In this paper, we present two new algebraic algorithms for the solution of the discrete algebraic Riccati equation. The first algorithm requires the nonsingularity of the transition matrix and is based on the solution of a standard eigenvalue problem for a new symplectic matrix; the proposed algorithm computes the extreme solutions of the discrete algebraic Riccati equation. The second algorithm solves the Riccati equation without the assumption of the nonsingularity of the transition matrix; the...
Non-trivial solutions to certain matrix equations.
Norm estimates for functions of two non-commuting matrices.
Norm estimates for solutions of matrix equations AX-XB=C and X-AXB=C
Let A, B and C be matrices. We consider the matrix equations Y-AYB=C and AX-XB=C. Sharp norm estimates for solutions of these equations are derived. By these estimates a bound for the distance between invariant subspaces of matrices is obtained.
Norms of matrix powers
Note on the numerical solutions of the general matrix convolution equations by using the iterative methods and box convolution product.