A class of Hamiltonian-symplectic methods for solving the algebraic Riccati equation

Application of Iterative Methods for Solving General Riccati Equation

An exponential spline for solving the fractional riccati differential equation

In this Article, proposes an approximation for the solution of the Riccati equation based on the use of exponential spline functions. Then the exponential spline equations are obtained and the differential equation of the fractional Riccati is discretized. The effect of performing this mathematical operation is obtained from an algebraic system of equations. To illustrate the benefits of the me...

Efficient methods for solving a nonsymmetric algebraic Riccati equation arising in stochastic fluid models

We consider the nonsymmetric algebraic Riccati equation XM12X + XM11 + M22X + M21 = 0, where M11,M12,M21,M22 are real matrices of sizes n × n, n × m,m × n, m × m, respectively, and M = [Mij ]i,j=1 is an irreducible singular M matrix with zero row sums. The equation plays an important role in the study of stochastic fluid models, where the matrix −M is the generator of a Markov chain. The soluti...

application of iterative methods for solving general riccati equation

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Solving the Algebraic Riccati Equation with the Matrix Sign Function

This paper presents solne inrprovements to the matrix-sigll-fllnction algorithn~ for the alge\,raic Riccati equation. A simple reorganization changes nonsynnnetric watrix inversion5 into syinmetric niatrix inversions. Scaling accelerates convergence of the basic iteration ant1 yields a new qnadratic formula for certain 2-by-2 algebraic Riccati eqnation5. Numerical experience suggests the algori...