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Systems & Control Letters, ISSN 0167-6911, 05/2019, Volume 127, pp. 35 - 38
We consider Homogeneous Algebraic Riccati Equations in the general situation when the matrix of the dynamics can be . We show that in this case the equation... 
Invariant subspaces | Homogeneous algebraic Riccati equation | Symmetric matrices
Journal Article
Journal of Computational and Applied Mathematics, ISSN 0377-0427, 12/2019, Volume 361, pp. 130 - 143
We consider the numerical solution of large-scale algebraic Riccati equations with high-rank constant terms. The solutions are not numerically low-rank, so the... 
Algebraic Riccati equation | Feedback gain | High-rank constant term | Large-scale problem | LQR optimal control | MATHEMATICS, APPLIED | ITERATIVE SOLUTIONS | PARAMETER-ESTIMATION | SYSTEMS | MATRIX EQUATIONS | DOUBLING-ALGORITHM | Algorithms
Journal Article
Applied Numerical Mathematics, ISSN 0168-9274, 11/2019
Journal Article
Journal of Computational and Applied Mathematics, ISSN 0377-0427, 06/2020, Volume 371, p. 112685
Journal Article
Journal of Computational and Applied Mathematics, ISSN 0377-0427, 04/2020, Volume 368, p. 112567
In this paper, based on the study of fluid flow models modulated by a Markov chain, we propose a new class of complex nonsymmetric algebraic Riccati equations... 
Extremal solution | Newton’s method | Basic fixed-point iterative method | Doubling algorithm | Preprocessing technique | H-matrix algebraic Riccati equation (HARE)
Journal Article
Linear Algebra and Its Applications, ISSN 0024-3795, 08/2017, Volume 527, pp. 184 - 215
We give a rank characterization of the solution set of discrete algebraic Riccati equations (DAREs) involving real matrices. Our characterization involves the... 
Discrete Lyapunov equation | Difference Riccati equation | Discrete algebraic Riccati equation | Non-symmetric algebraic Riccati equation | Schur complement | BERNOULLI EQUATIONS | MATHEMATICS | MATHEMATICS, APPLIED | NUMERICAL-SOLUTION | PARAMETRIZATION | Electrical engineering | Electric properties
Journal Article
Linear Algebra and its Applications, ISSN 0024-3795, 08/2017, Volume 527, p. 184
We give a rank characterization of the solution set of discrete algebraic Riccati equations (DAREs) involving real matrices. Our characterization involves the... 
Matrix | Algebra | Mathematical analysis | Integral equations | Integrals | Algebraic group theory | Subspaces | Riccati equation | Invariants
Journal Article
Applied Mathematics and Computation, ISSN 0096-3003, 04/2019, Volume 347, pp. 442 - 448
Research on the theories and efficient numerical methods of M-matrix algebraic Riccati equation (MARE) has become a hot topic in recent years. In this paper,... 
Minimal nonnegative solution | ALI iteration method | M-matrix algebraic Riccati equation | Newton method | MATHEMATICS, APPLIED | WIENER-HOPF FACTORIZATION | PRESERVING DOUBLING-ALGORITHM
Journal Article
Journal of Computational and Applied Mathematics, ISSN 0377-0427, 08/2018, Volume 338, pp. 91 - 110
Algebraic Riccati equations are encountered in many applications of control and engineering problems, e.g., LQG problems and control theory. In this work, we... 
[formula omitted]-superlinear with order [formula omitted] | Doubling algorithm | Sherman morrison woodbury formula | Algebraic Riccati equations | Semigroup property | Positive definite solution | r-superlinear with order r | MATHEMATICS, APPLIED | POSITIVE-DEFINITE SOLUTIONS | CONVERGENCE | COMPUTATION | DOUBLING-ALGORITHM
Journal Article
Computers and Mathematics with Applications, ISSN 0898-1221, 07/2018, Volume 76, Issue 1, pp. 187 - 203
In this paper we consider a family of high-order iterative methods which is more efficient than the Newton method to approximate a solution of symmetric... 
High order iterative schemes | Algebraic Riccati equations | Local convergence | Lyapunov equations | MATHEMATICS, APPLIED | NUMERICAL-SOLUTION | EFFICIENCY
Journal Article
Linear Algebra and Its Applications, ISSN 0024-3795, 10/2016, Volume 507, pp. 356 - 372
We give a new characterization of the solution set of non-symmetric algebraic Riccati equations involving real matrices. Our characterization involves the use... 
Poset | Non-symmetric algebraic Riccati equation | Sylvester equation | M-MATRICES | MATHEMATICS | MATHEMATICS, APPLIED | FACTORIZATION | Electrical engineering | Electric properties
Journal Article
Journal of Computational and Applied Mathematics, ISSN 0377-0427, 08/2017, Volume 319, pp. 352 - 364
Fast iterative algorithms for computing interval matrices containing solutions of discrete-time algebraic Riccati equations are proposed. These algorithms... 
Algebraic Riccati equations | Stabilizing solution | Verified computation | MATHEMATICS, APPLIED | Algorithms
Journal Article
Applied Mathematics and Computation, ISSN 0096-3003, 12/2017, Volume 314, pp. 80 - 97
This paper is devoted to a structured perturbation analysis of the symmetric algebraic Riccati equations by exploiting the symmetry structure. Based on the... 
Condition number | Statistical condition estimation | Symmetric algebraic Riccati equation | Perturbation analysis | MATHEMATICS, APPLIED | LINEAR LEAST-SQUARES | COMPONENTWISE CONDITION NUMBERS | SYSTEMS | Statistics | Analysis | Algorithms
Journal Article
Journal of Computational and Applied Mathematics, ISSN 0377-0427, 03/2017, Volume 313, pp. 515 - 535
We describe a procedure based on the Krawczyk method to compute a verified enclosure for the stabilizing solution of a continuous-time algebraic Riccati... 
Algebraic Riccati equation | Stabilizing solution | Verified computation | Krawczyk’s method | Interval arithmetic | Krawczyk's method | MATHEMATICS, APPLIED | ENCLOSURES | COMPUTATION | Applications of mathematics | State of the art | Algebra | Mathematical analysis | Benchmarking | Mathematical models | Riccati equation | Standards
Journal Article
ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS, ISSN 1292-8119, 01/2018, Volume 24, Issue 1, pp. 129 - 151
Journal Article
Mediterranean Journal of Mathematics, ISSN 1660-5446, 12/2016, Volume 13, Issue 6, pp. 4961 - 4973
Journal Article
Journal of Computational and Applied Mathematics, ISSN 0377-0427, 01/2013, Volume 237, Issue 1, pp. 373 - 383
We consider the solution of large-scale algebraic Riccati equations with numerically low-ranked solutions. For the discrete-time case, the structure-preserving... 
Doubling algorithm | Krylov subspace | Large-scale problem | Continuous-time algebraic Riccati equation | MATHEMATICS, APPLIED | ALGORITHMS | Algorithms | Algebra | Computation | Mathematical analysis | Mathematical models | Riccati equation | Iterative methods | Matlab
Journal Article
Linear Algebra and Its Applications, ISSN 0024-3795, 01/2016, Volume 488, pp. 430 - 459
This article discusses an approach to solving large-scale algebraic Riccati equations (AREs) by computing a low-dimensional stable invariant subspace of the... 
Hamiltonian matrices | Invariant subspaces | Matrix equations | Krylov subspaces | Algebraic Riccati equations | ADI iteration | MATHEMATICS, APPLIED | FACTORIZATIONS | LYAPUNOV EQUATIONS | RANK | MATHEMATICS | KRYLOV SUBSPACE | SINGULAR-VALUES | Algorithms
Journal Article
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