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In this paper, we first give a result which links any global Krylov method for solving linear systems with several right-hand sides to the corresponding classical Krylov method. Then, we propose a general framework for matrix Krylov subspace methods for linear systems with multiple right-hand sides. Our approach use global projection techniques, it is based(More)
In this paper, we introduce two new methods for solving large sparse nonsymmetric linear systems with several right-hand sides. These methods are the global Hessenberg and global CMRH methods. Using the global Hessenberg process, these methods are less expensive than the global FOM and global GMRES methods [9]. Theoretical results about the new methods are(More)
In this paper, we give and analyze a Finite Difference version of the Generalized Hessenberg (FDGH) method. The obtained results show that applying this method in solving a linear system is equivalent to applying the Generalized Hessenberg method to a perturbed system. The finite difference version of the Generalized Hessenberg method is used in the context(More)
Algebraic Riccati equations (discrete-time or continuous-time) play a fundamental role in many problems in control theory. They arise in linear-quadratic regulator problems, H ∞ or H 2-control, model reduction problems and many others. In this talk we propose numerical methods for large discrete-time algebraic Riccati equations (DARE). We present block(More)
The aim of the present paper is to give some new algebraic properties of the extended block and the extended global Arnoldi algorithms. These results are then applied on moment matching methods for model reductions in large-scale dynamical systems to get low-order models that approximate the original models by matching moments and Markov parameters at the(More)
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