Related papers: Homographic scheme for Riccati equation
We present a Lagrange-Galerkin scheme free from numerical quadrature for convection-diffusion problems. Since the scheme can be implemented exactly as it is, theoretical stability result is assured. While conventional Lagrange-Galerkin…
In this paper, we focus on using optimization methods to solve matrix equations by transforming the problem of solving the Sylvester matrix equation or continuous algebraic Riccati equation into an optimization problem. Initially, we use a…
We derive some analytic closed-form solutions for a class of Riccati equation y'(x)-\lambda_0(x)y(x)\pm y^2(x)=\pm s_0(x), where \lambda_0(x), s_0(x) are C^{\infty}-functions. We show that if \delta_n=\lambda_n s_{n-1}-\lambda_{n-1}s_n=0,…
Several instances of integrable Riccati equations are analyzed from the geometric perspective of the theory of Lie systems. This provides us a unifying viewpoint for previous approaches.
How to develop efficient numerical schemes while preserving the energy stability at the discrete level is a challenging issue for the three component Cahn-Hilliard phase-field model. In this paper, we develop first and second order temporal…
We study the effect of global error control in the numerical solution of Hamiltonian systems. In particular, we apply the RKQ algorithm in the numerical solution of a Hamiltonian system. This algorithm is designed to provide stepwise…
A new numerical scheme for conservation equations based on evolution by asynchronous discrete events is presented. During each event of the scheme only two cells of the underlying Cartesian grid are active, and an event is processed as the…
In this paper, a large class of time-varying Riccati equations arising in stochastic dynamic games is considered. The problem of the existence and uniqueness of some globally defined solution, namely the bounded and stabilizing solution, is…
In this paper we study the continuous dependence with respect to obstacles for obstacle problems with measure data. This is deeply investigated introducing a suitable type of convergence, which gives stability under very general hypotheses.…
The effectiveness of the hyperbolic relaxation method for solving the Einstein constraint equations numerically is studied here on a variety of compact orientable three-manifolds. Convergent numerical solutions are found using this method…
This paper is concerned with the linear quadratic (LQ) optimal control of continuous-time system with terminal state constraint. In particular, multiple agents exist in the system which can only access partial information of the matrix…
Model order reduction algorithms for large-scale descriptor systems are proposed using balanced truncation, in which symmetry or block skew symmetry (reciprocity) and the positive realness of the original transfer matrix are preserved. Two…
In this paper, we present a fast and accurate numerical scheme for the solution of fifth-order boundary-value problems. We apply the reproducing kernel Hilbert space method (RKHSM) for solving this problem. The analytic results of the…
Linear-quadratic optimal control problem for systems governed by forward-backward stochastic differential equations has been extensively studied over the past three decades. Recent research has revealed that for forward-backward control…
In this paper, we derive a Riccati-type equation applicable to (sub-)static Einstein spaces and examine its various applications. Specifically, within the framework of conformally compactifiable manifolds, we prove a splitting theorem for…
Schemes for exact multiplication of small matrices have a large symmetry group. This group defines an equivalence relation on the set of multiplication schemes. There are algorithms to decide whether two schemes are equivalent. However, for…
The stability of a recently developed piecewise flat Ricci flow is investigated, using a linear stability analysis and numerical simulations, and a class of piecewise flat approximations of smooth manifolds is adapted to avoid an inherent…
We present certain techniques to find completely positive maps between matrix algebras that take prescribed values on given data. To this aim we describe a semidefinite programming approach and another convex minimization method supported…
Contraction properties of the Riccati operator are studied within the context of non-stationary linear-quadratic optimal control. A lifting approach is used to obtain a bound on the rate of strict contraction, with respect to the Riemannian…
In this paper, we propose an RADI-type method for large-scale stochastic continuous-time algebraic Riccati equations with sparse and low-rank matrices. This new variant of RADI-type methods is developed by integrating the core concept of…