A low-rank Krylov squared Smith method for large-scale discrete-time Lyapunov equations
نویسندگان
چکیده
منابع مشابه
Solution of Large - Scale Lyapunov Equations via the Block Modified Smith Method
Solution of Large-Scale Lyapunov Equations via the Block Modified Smith Method by John Sabino Balanced truncation is an attractive method for reducing the dimension of mediumscale dynamical systems. Research in recent years has brought approximate balanced truncation to the large-scale setting. At the heart of this technique are alternating direction implicit (ADI) methods for solving large Lya...
متن کاملLow - Rank Solution Methods for Large - Scale Linear Matrix Equations
LOW-RANK SOLUTION METHODS FOR LARGE-SCALE LINEAR MATRIX EQUATIONS Stephen D. Shank DOCTOR OF PHILOSOPHY Temple University, May, 2014 Professor Daniel B. Szyld, Chair We consider low-rank solution methods for certain classes of large-scale linear matrix equations. Our aim is to adapt existing low-rank solution methods based on standard, extended and rational Krylov subspaces to solve equations w...
متن کاملLow Rank Solution of Lyapunov Equations
This paper presents the Cholesky factor–alternating direction implicit (CF–ADI) algorithm, which generates a low rank approximation to the solution X of the Lyapunov equation AX + XAT = −BBT . The coefficient matrix A is assumed to be large, and the rank of the righthand side −BBT is assumed to be much smaller than the size of A. The CF–ADI algorithm requires only matrix-vector products and mat...
متن کاملKrylov subspace methods for projected Lyapunov equations
We consider the numerical solution of projected Lyapunov equations using Krylov subspace iterative methods. Such equations play a fundamental role in balanced truncation model reduction of descriptor systems. We present generalizations of the extended block and global Arnoldi methods to projected Lyapunov equations and compare these methods with the alternating direction implicit method with re...
متن کاملA preconditioned low-rank CG method for parameter-dependent Lyapunov matrix equations
This paper is concerned with the numerical solution of symmetric large-scale Lyapunov equations with low-rank right-hand sides and coefficient matrices depending on one or several parameters. Specifically, we consider the situation when the parameter dependence is sufficiently smooth and the aim is to compute solutions for many different parameter samples. Based on existing results for Lyapunov...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2012
ISSN: 0024-3795
DOI: 10.1016/j.laa.2011.07.021