Low-rank iterative methods for projected generalized Lyapunov equations.
Mathematical basis of a system supporting interconnection design.
Matrix bounds for the solution of the continuous algebraic Riccati equation.
Matrix computation and the theory of moments.
Matrix rank certification.
Matrix transformations and quasi-Newton methods.
Maximal solutions of two–sided linear systems in max–min algebra
Max-min algebra and its various aspects have been intensively studied by many authors [1, 4] because of its applicability to various areas, such as fuzzy system, knowledge management and others. Binary operations of addition and multiplication of real numbers used in classical linear algebra are replaced in max-min algebra by operations of maximum and minimum. We consider two-sided systems of max-min linear equations , with given coefficient matrices and . We present a polynomial method for...
Methods for solving some parameter problems of algebra.
Monotone convergence of the Lanczos approximations to matrix functions of Hermitian matrices.
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.
Newton iteration for the closest normal matrix of order two.
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...
Note on the numerical solutions of the general matrix convolution equations by using the iterative methods and box convolution product.
Nový pohled na numerický výpočet největšího společného dělitele dvou polynomů
Numerical determination of a canonical form of a symplectic matrix.
Numerical operations among rational matrices: standard techniques and interpolation
Numerical operations on and among rational matrices are traditionally handled by direct manipulation with their scalar entries. A new numerically attractive alternative is proposed here that is based on rational matrix interpolation. The procedure begins with evaluation of rational matrices in several complex points. Then all the required operations are performed consecutively on constant matrices corresponding to each particular point. Finally, the resulting rational matrix is recovered from the...
Numerically stable algorithm for pole assignment of linear single-input systems
On a Class of Jacobi-Like Procedures for Diagonalising Arbitrary Real Matrices.
On a New Class of Elementary Matrices.
On an algorithm for testing T4 solvability of max-plus interval systems
In this paper, we shall deal with the solvability of interval systems of linear equations in max-plus algebra. Max-plus algebra is an algebraic structure in which classical addition and multiplication are replaced by and , where , . The notation represents an interval system of linear equations, where and are given interval matrix and interval vector, respectively. We can define several types of solvability of interval systems. In this paper, we define the T4 solvability and give an algorithm...