CONVERGENCE ANALYSIS OF PROJECTION METHODS FOR THE NUMERICAL SOLUTION OF LARGE LYAPUNOV EQUATIONS

被引：27

作者：

Simoncini, V. ^{[1
]}

Druskin, V. ^{[2
]}

机构：

[1] Univ Bologna, Dipartimento Matemat, I-40127 Bologna, Italy

[2] Schlumberger Doll Res Ctr, Cambridge, MA 02139 USA

来源：

SIAM JOURNAL ON NUMERICAL ANALYSIS | 2009年 / 47卷 / 02期

关键词：

Lyapunov equation; Krylov subspace; matrix exponential; Faber polynomials; KRYLOV SUBSPACE METHODS; FABER POLYNOMIALS; SUPERLINEAR CONVERGENCE; MATRIX EQUATIONS; APPROXIMATION; GMRES;

D O I：

10.1137/070699378

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The numerical solution of large-scale continuous-time Lyapunov matrix equations is of great importance in many application areas. Assuming that the coefficient matrix is positive definite, but not necessarily symmetric, in this paper we analyze the convergence of projection-type methods for approximating the solution matrix. Under suitable hypotheses on the coefficient matrix, we provide new asymptotic estimates for the error matrix when a Galerkin method is used in a Krylov subspace. Numerical experiments confirm the good behavior of our upper bounds when linear convergence of the solver is observed.

引用

页码：828 / 843

页数：16

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