Convergence analysis of the extended Krylov subspace method for the Lyapunov equation
نویسندگان
چکیده
The Extended Krylov Subspace Method has recently arisen as a competitive method for solving large-scale Lyapunov equations. Using the theoretical framework of orthogonal rational functions, in this paper we provide a general a-priori error estimate when the known term has rankone. Special cases, such as symmetric coefficient matrix, are also treated. Numerical experiments confirm the proved theoretical assertions.
منابع مشابه
Preconditioned Generalized Minimal Residual Method for Solving Fractional Advection-Diffusion Equation
Introduction Fractional differential equations (FDEs) have attracted much attention and have been widely used in the fields of finance, physics, image processing, and biology, etc. It is not always possible to find an analytical solution for such equations. The approximate solution or numerical scheme may be a good approach, particularly, the schemes in numerical linear algebra for solving ...
متن کاملAnalysis of the Rational Krylov Subspace and ADI Methods for Solving the Lyapunov Equation
For large scale problems, an effective approach for solving the algebraic Lyapunov equation consists of projecting the problem onto a significantly smaller space and then solving the reduced order matrix equation. Although Krylov subspaces have been used for long time, only more recent developments have shown that rational Krylov subspaces can be a competitive alternative to the classical and v...
متن کاملKrylov Subspace Type Methods for Solving Projected Generalized Continuous-Time Lyapunov Equations
In this paper we consider the numerical solution of projected generalized continuous-time Lyapunov equations with low-rank right-hand sides. The interest in this problem stems from stability analysis and control problems for descriptor systems including model reduction based on balanced truncation. Two projection methods are proposed for calculating low-rank approximate solutions. One is based ...
متن کاملEfficient low-rank solution of generalized Lyapunov equations
An iterative method for the low-rank approximate solution of a class of generalized Lyapunov equations is studied. At each iteration, a standard Lyapunov is solved using Galerkin projection with an extended Krylov subspace method. This Lyapunov equation is solved inexactly, thus producing a nonstationary iteration. Several theoretical and computational issues are discussed so as to make the ite...
متن کاملA Class of Nested Iteration Schemes for Generalized Coupled Sylvester Matrix Equation
Global Krylov subspace methods are the most efficient and robust methods to solve generalized coupled Sylvester matrix equation. In this paper, we propose the nested splitting conjugate gradient process for solving this equation. This method has inner and outer iterations, which employs the generalized conjugate gradient method as an inner iteration to approximate each outer iterate, while each...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Numerische Mathematik
دوره 118 شماره
صفحات -
تاریخ انتشار 2011