A
André C. M. Ran
Researcher at VU University Amsterdam
Publications - 202
Citations - 4299
André C. M. Ran is an academic researcher from VU University Amsterdam. The author has contributed to research in topics: Matrix (mathematics) & Algebraic Riccati equation. The author has an hindex of 30, co-authored 195 publications receiving 4075 citations. Previous affiliations of André C. M. Ran include North-West University & University of Amsterdam.
Papers
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A fixed point theorem in partially ordered sets and some applications to matrix equations
TL;DR: In this paper, an analogue of Banach's fixed point theorem in partially ordered sets is proved, and several applications to linear and nonlinear matrix equations are discussed, including the application of the Banach theorem to the Partially ordered Set (POPS) problem.
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Necessary and sufficient conditions for the existence of a positive definite solution of the matrix equation X + A*X-1A = Q
TL;DR: In this article, the authors considered the problem of finding a positive definite solution of the matrix equation X + A ∗ X -1 A = Q in a special case of the discrete-time Riccati equation.
Journal ArticleDOI
Existence and comparison theorems for algebraic Riccati equations for continuous- and discrete-time systems
André C. M. Ran,R. Vreugdenhil +1 more
TL;DR: In this paper, two comparison theorems for algebraic Riccati equations of the form XBR -1 B ∗ X−X(A−BR −1 C) -(A −BR − 1 C) ∗X−Q−C ∗ R -1 C = 0 were discussed.
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On an Iteration Method for Solving a Class of Nonlinear Matrix Equations
TL;DR: It is shown that under some conditions an iteration method converges to a positive definite solution of a set of equations of the form X+A^{\star}{\cal F}(X)A =Q, where A is arbitrary and Q is apositive definite matrix.
Book
Factorization of Matrix and Operator Functions: The State Space Method
TL;DR: Stability of Factorization and of Invariant Subspaces, Stability of Spectral Divisors, and Factorization of Real Matrix Functions.