Sylvester equations and projection-based model reduction
نویسندگان
چکیده
منابع مشابه
Projection methods for large T-Sylvester equations
The matrix Sylvester equation for congruence, or T-Sylvester equation, has recently attracted considerable attention as a consequence of its close relation to palindromic eigenvalue problems. The theory concerning T-Sylvester equations is rather well understood and there are stable and efficient numerical algorithms which solve these equations for smallto medium-sized matrices. However, develop...
متن کاملProjection methods for large-scale T-Sylvester equations
The matrix Sylvester equation for congruence, or T-Sylvester equation, has recently attracted considerable attention as a consequence of its close relation to palindromic eigenvalue problems. The theory concerning T-Sylvester equations is rather well understood and there are stable and efficient numerical algorithms which solve these equations for smallto medium-sized matrices. However, develop...
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To be feasible for computationally intensive applications such as parametric studies, optimization, and control design, large-scale finite element analysis requires model order reduction. This is particularly true in nonlinear settings that tend to dramatically increase computational complexity. Although significant progress has been achieved in the development of computational approaches for t...
متن کاملA Projection Method Based on Extended Krylov Subspaces for Solving Sylvester Equations
In this paper we study numerical methods for solving Sylvester matrix equations of the form AX +XB +CD = 0. A new projection method is proposed. The union of Krylov subspaces in A and its inverse and the union of Krylov subspaces in B and its inverse are used as the right and left projection subspaces, respectively. The Arnoldi-like process for constructing the orthonormal basis of the projecti...
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In this paper, we describe some recent developments in the use of projection methods to produce reduced-order models for linear time-invariant dynamic systems. Previous related eeorts in model reduction problems from various applications are also discussed. An overview is given of the theory governing the deenition of the family of Rational Krylov methods, the practical heuristics involved and ...
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ژورنال
عنوان ژورنال: Journal of Computational and Applied Mathematics
سال: 2004
ISSN: 0377-0427
DOI: 10.1016/j.cam.2003.08.026