Related papers: On the Solution of the Nonsymmetric T-Riccati Equa…
The problem of block diagonalization for diagonally dominant symmetric block operator matrices with self-adjoint diagonal entries is considered. We show that a reasonable block diagonalization with respect to a reducing graph subspace…
The differential Riccati equation appears in different fields of applied mathematics like control and system theory. Recently Galerkin methods based on Krylov subspaces were developed for the autonomous differential Riccati equation. These…
A recent problem [B. Gardas, J. Math. Phys. 52, 042104 (2011)] concerning an antilinear solution of the Riccati equation is solved. We also exemplify that a simplification of the Riccati equation, even under reasonable assumptions, can lead…
An abstract nonautonomous parabolic linear-quadratic regulator problem with very general final cost operator P_T is considered, subject to the same assumptions under which a classical solution of the associated differential Riccati equation…
This paper considers large-scale nonsymmetric continuous-time algebraic Riccati equations (NAREs) that admit low-rank solutions. Low-rank alternating direction implicit (ADI) methods have proven to be an efficient approach for solving…
We are concerned with the tensor equation with an M-tensor or Z-tensor, which we call the M- tensor equation or Z-tensor equation respectively. We derive a necessary and sufficient condition for a Z (or M)-tensor equation to have…
The Total Least Squares solution of an overdetermined, approximate linear equation $Ax \approx b$ minimizes a nonlinear function which characterizes the backward error. We show that a globally convergent variant of the Gauss--Newton…
An inexact Newton type method for numerical minimization of convex piecewise quadratic functions is considered and its convergence is analyzed. Earlier, a similar method was successfully applied to optimizaton problems arising in numerical…
The scalar Riccati equation is a prototypical nonlinear ODE having diverse mathematical connections. In the centuries since its initial formulation, a standard textbook theory has emerged according to which the general solution may be…
Nonlinear matrix equations arise in many practical contexts related to control theory, dynamical programming and finite element methods for solving some partial differential equations. In most of these applications, it is needed to compute…
We consider approximations to the solutions of differential Riccati equations in the context of linear quadratic regulator problems, where the state equation is governed by a multiscale operator. Similarly to elliptic and parabolic…
The joint approximate diagonalization of non-commuting symmetric matrices is an important process in independent component analysis. This problem can be formulated as an optimization problem on the Stiefel manifold that can be solved using…
In this work, a new algorithm for solving symmetric indefinite systems of linear equations is presented. It factorizes the matrix into the form LDLt using Jacobi rotations in order to increase the pivot's absolute value. Furthermore, Rook's…
In a recent paper by Chen et al. [8], the authors initiated the control-theoretic study of a class of discrete-time multilinear time-invariant (MLTI) control systems, where system states, inputs, and outputs are all tensors endowed with the…
The block operator matrix theory is used to investigate the problem of a single qubit. We will establish a connection between the Riccati operator equation and the possibility of obtaining an exact reduced dynamics for the qubit in…
Solving large-scale continuous-time algebraic Riccati equations is a significant challenge in various control theory applications. This work demonstrates that when the matrix coefficients of the equation are quasiseparable, the solution…
A three-dimensional Riccati differential equation of complex quaternion-valued functions is studied. Many properties similar to those of the ordinary differential Riccati equation such that linearization and Picard theorem are obtained. Lie…
We have recently presented a method to solve an overdetermined linear system of equations with multiple right hand side vectors, where the unknown matrix is to be symmetric and positive definite. The coefficient and the right hand side…
In this paper, we consider nonsymmetric solutions to certain Lyapunov and Riccati equations and inequalities with coefficient matrices corresponding to cone-preserving dynamical systems. Most results presented here appear to be novel even…
In the present paper a numerical method is developed to approximate the solution of two-dimensional NLS equation in the presence of a singular potential. The method leads to Lyapunov-Syslvester algebraic operators that are shown to be…