Interpolation schemes for collocation solutions of two point boundary value problems
SIAM Journal on Scientific and Statistical Computing
Topics in matrix analysis
A high-order method for stiff boubdary value problems with turning points
SIAM Journal on Scientific and Statistical Computing
Numerical integration of the differential Riccati equation and some related issues
SIAM Journal on Numerical Analysis
Using MPI: portable parallel programming with the message-passing interface
Using MPI: portable parallel programming with the message-passing interface
ScaLAPACK user's guide
Solution of the matrix equation AX + XB = C [F4]
Communications of the ACM
Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations
Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations
A Proposal for a Set of Parallel Basic Linear Algebra Subprograms
A Proposal for a Set of Parallel Basic Linear Algebra Subprograms
LAPACK Working Note 37: Two Dimensional Basic Linear Algebra Communication Subprograms
LAPACK Working Note 37: Two Dimensional Basic Linear Algebra Communication Subprograms
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Differential Riccati equations play a fundamental role in control theory, for example, optimal control, filtering and estimation, decoupling and order reduction, etc. In this paper several algorithms for solving differential Riccati equations based on Adams-Bashforth and Adams-Moulton methods are described. The Adams-Bashforth methods allow us explicitly to compute the approximate solution at an instant time from the solutions in previous instants. In each step of Adams-Moulton methods an algebraic matrix Riccati equation (AMRE) is obtained, which is solved by means of Newton's method. Nine algorithms are considered for solving the AMRE: a Sylvester algorithm, an iterative generalized minimum residual (GMRES) algorithm, a fixed-point algorithm and six combined algorithms. Since the above algorithms have a similar structure, it is possible to design a general and efficient algorithm that uses one algorithm or another depending on the considered differential matrix Riccati equation. MATLAB versions of the above algorithms are developed, comparing precision and computational costs, after numerous tests on five case studies.