A GMRES-based BDF method for solving differential Riccati equations

DOI10.1016/j.amc.2007.06.021zbMath1135.65340OpenAlexW1967747361MaRDI QIDQ2479126

Jacinto-Javier Ibáñez, Enrique Arias, Jesús Peinado, Vicente G. Hernández

Publication date: 26 March 2008

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.amc.2007.06.021

zbMATH Keywords

Newton's methodalgebraic Riccati equationnumerical examplesBDF methodsSylvester equationGMRES methodsbackward differentiation formula (BDF) methodsdifferential Riccati equationsBartels-Stewart methodgeneralized minimum residual (GMRES) method

Mathematics Subject Classification ID

Numerical computation of solutions to systems of equations (65H10) Nonlinear ordinary differential equations and systems (34A34) Iterative numerical methods for linear systems (65F10) Numerical methods for initial value problems involving ordinary differential equations (65L05) Finite difference and finite volume methods for ordinary differential equations (65L12)

Related Items

An extended block Golub-Kahan algorithm for large algebraic and differential matrix Riccati equations, Adams-Bashforth and Adams-Moulton methods for solving differential Riccati equations, Solving differential matrix Riccati equations by a piecewise-linearized method based on diagonal Padé approximants

Uses Software

• LAPACK
• ScaLAPACK
• BLAS
• ITSOL
• MPI
• SPARSKIT
• ODEPACK
• Algorithm 432

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Initial value methods for boundary value problems. Theory and application of invariant imbedding
• A fixed point-based BDF method for solving differential Riccati equations
• Efficient matrix-valued algorithms for solving stiff Riccati differential equations
• A canonical form and solution for the matrix Riccati differential equation
• Numerical integration of the differential matrix Riccati equation
• Superposition laws for solutions of differential matrix Riccati equations arising in control theory
• Algorithm 656: an extended set of basic linear algebra subprograms: model implementation and test programs
• Numerical Integration of the Differential Riccati Equation and Some Related Issues
• Generalized Chandrasekhar algorithms: Time-varying models
• Kronecker products and matrix calculus in system theory
• ScaLAPACK Users' Guide
• Algorithm 432 [C2: Solution of the matrix equation AX + XB = C [F4]]
• Algorithm 842
• The numerical solution of the matrix Riccati differential equation