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Riccati equation

About: Riccati equation is a research topic. Over the lifetime, 10428 publications have been published within this topic receiving 210015 citations. The topic is also known as: Riccati's differential equation.


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01 Jan 2008
TL;DR: A new iterative method for the computation of approximate solutions to large-scale continuous-time algebraic Riccati equations through a projection method onto an extended block Krylov subspace is presented.
Abstract: We present a new iterative method for the computation of approximate solutions to large-scale continuous-time algebraic Riccati equations. The proposed method is a projection method onto an extended block Krylov subspace, which can be seen as a sum of two block Krylov subspaces in A and A 1 . We give some the- oretical results and present numerical experiments for large and sparse problems. These numerical tests show the efficiency of the proposed scheme as compared to the block Arn oldi and Newton-ADI methods.

87 citations

Journal ArticleDOI
TL;DR: In this article, the authors explored the use of a discrete singular convolution algorithm as a unified approach for numerical integration of the Fokker-Planck equation and demonstrated that different implementations of the present algorithm, such as global, local, Galerkin, collocation and finite difference, can be deduced from a single starting point.
Abstract: This paper explores the use of a discrete singular convolution algorithm as a unified approach for numerical integration of the Fokker-Planck equation. The unified features of the discrete singular convolution algorithm are discussed. It is demonstrated that different implementations of the present algorithm, such as global, local, Galerkin, collocation and finite difference, can be deduced from a single starting point. Three benchmark stochastic systems, the repulsive Wong process, the Black-Scholes equation and a genuine nonlinear model, are employed to illustrate the robustness and to test the accuracy of the present approach for the solution of the Fokker-Planck equation via a time-dependent method. An additional example, the incompressible Euler equation, is used to further validate the present approach for more difficult problems. Numerical results indicate that the present unified approach is robust and accurate for solving the Fokker-Planck equation.

87 citations

Journal ArticleDOI
TL;DR: In this article, a new transformation between two integrable hierarchies of the Camassa-Holm equation and the Hunter-Saxton equation is presented, which is the high-frequency limit of the CAMASHA-HOLM equation.
Abstract: In this article we present a new transformation between two integrable hierarchies of the Camassa-Holm equation and the Hunter-Saxton equation. For instance we present a transformation between the Harry-Dym equation and the extended Harry-Dym equation. Moreover, we describe a relationship between the Hunter-Saxton equation, which is the high-frequency limit of the Camassa-Holm equation, and the Sinh-Gordon equation by a reciprocal transformation.

87 citations

01 Jan 2004
TL;DR: The linear quadratic optimization problem for a class of linear stochastic systems subject both to multiplicative white noise and Markovian jumping is investigated and an iterative procedure to compute the maximal solution of the systems of generalized Riccati equations is provided.
Abstract: In this paper, the linear quadratic optimization problem for a class of linear stochastic systems subject both to multiplicative white noise and Markovian jumping is investigated. Two classes of admissible controls are considered. One of these classes contains controls with additional property that corre- sponding trajectories tend to zero (in mean square) when tends to , while concerning the controls contained in the second class of admissible controls there is not any stability assumption. In the optimization problem over the first class of admissible controls, the cost functional could have indefinite sign of weights matrices. An iterative procedure to compute the maximal solution of the systems of generalized Riccati equations is provided. A numerical example to illustrate the applicability of the iterative procedure is given.

87 citations

Journal ArticleDOI
TL;DR: The covariance equation based on second-order closure for dynamics governed by a general scalar nonlinear partial differential equation (PDE) is studied in this paper, where it is shown that the covariance can be solved approximately, to any desired accuracy, by solving instead an auxiliary system of PDEs in just n dimensions.
Abstract: The covariance equation based on second-order closure for dynamics governed by a general scalar nonlinear partial differential equation (PDE) is studied. If the governing dynamics involve n space dimensions, then the covariance equation is a PDE in 2n space dimensions. Solving this equation for n = 3 is therefore computationally infeasible. This is a hindrance to stochastic-dynamic prediction as well as to novel methods of data assimilation based on the Kalman filter. It is shown that the covariance equation can be solved approximately, to any desired accuracy, by solving instead an auxiliary system of PDEs in just n dimensions. The first of these is a dynamical equation for the variance field. Successive equations describe, to increasingly high order, the dynamics of the shape of either the covariance function or the correlation function for points separated by small distances. The second-order equation, for instance, describes the evolution of the correlation length (turbulent microscale) field...

87 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
2023153
2022335
2021203
2020240
2019223
2018231