On Weakly Formulated Sylvester Equations and Applications
نویسندگان
چکیده
منابع مشابه
On Weakly Formulated Sylvester Equations and Applications
We use a “weakly formulated” Sylvester equation H1/2TM−1/2 −H−1/2TM1/2 = F to obtain new bounds for the rotation of spectral subspaces of a nonnegative selfadjoint operator in a Hilbert space. Our bound extends the known results of Davis and Kahan. Another application is a bound for the square root of a positive selfadjoint operator which extends the known rule: “The relative error in the squar...
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In this paper we consider the numerical solution of large-scale projected generalized continuous-time and discrete-time Sylvester equations with low-rank right-hand sides. First, we present the results on the sufficient conditions for the existence, uniqueness, and analytic formula of the solutions of these equations. Second, we review the low-rank alternating direction implicit method and the ...
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The global FOM and GMRES algorithms are among the effective methods to solve Sylvester matrix equations. In this paper, we study these algorithms in the case that the coefficient matrices are real symmetric (real symmetric positive definite) and extract two CG-type algorithms for solving generalized Sylvester matrix equations. The proposed methods are iterative projection metho...
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Sylvester equations play a central role in many areas of applied mathematics and in particular in systems and control theory. Here we will show how low-rank solutions for stable Sylvester equations can be computed based on the matrix sign function method. We discuss applications in model reduction as well as in observer design. Numerical experiments demonstrate the efficiency of the proposed me...
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This paper is concerned with numerical solutions of large scale Sylvester equations AX −XB = C, Lyapunov equations as a special case in particular included, with C having very small rank. For stable Lyapunov equations, Penzl (2000) and Li andWhite (2002) demonstrated that the so called Cholesky factored ADI method with decent shift parameters can be very effective. In this paper we present a ge...
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ژورنال
عنوان ژورنال: Integral Equations and Operator Theory
سال: 2007
ISSN: 0378-620X,1420-8989
DOI: 10.1007/s00020-007-1482-4