A Reformulated Low-Rank ADI Iteration with Explicit Residual Factors
نویسندگان
چکیده
منابع مشابه
Finite-Rank ADI Iteration for Operator Lyapunov Equations
We give an algorithmic approach to the approximative solution of operator Lyapunov equations for controllability. Motivated by the successfully applied alternating direction implicit (ADI) iteration for matrix Lyapunov equations, we consider this method for the determination of Gramian operators of infinite-dimensional control systems. In the case where the input space is finitedimensional, thi...
متن کاملComputing real low-rank solutions of Sylvester equations by the factored ADI method
We investigate the factored ADI iteration for large and sparse Sylvester equations. A novel low-rank expression for the associated Sylvester residual is established which enables cheap computations of the residual norm along the iteration, and which yields a reformulated factored ADI iteration. The application to generalized Sylvester equations is considered as well. We also discuss the efficie...
متن کاملLow Rank ADI Solution of Sylvester Equation via Exact Shifts
The solution to a general Sylvester equation AX−XB = GF ∗ with a low rank righthand side is analyzed quantitatively through Low-rank Alternating-DirectionalImplicit method (LR-ADI) with exact shifts. New bounds and perturbation bounds on X are obtained. A distinguished feature of these bounds is that they reflect the interplay between the eigenvalue decompositions of A and B and the right-hand ...
متن کاملApproximate low-rank factorization with structured factors
An approximate rank revealing factorization problem with structure constraints on the normalized factors is considered. Examples of structure, motivated by an application in microarray data analysis, are sparsity, nonnegativity, periodicity, and smoothness. In general, the approximate rank revealing factorization problem is nonconvex. An alternating projections algorithm is developed, which is ...
متن کاملAnalysis of the solution of the Sylvester equation using low-rank ADI with exact shifts
The solution to a general Sylvester equation AX − XB = GF with a low-rank right-hand side is analyzed quantitatively through the Low-rank Alternating-Directional-Implicit method (LR-ADI) with exact shifts. New bounds and perturbation bounds on X are obtained. A distinguished feature of these bounds is that they reflect the interplay between the eigenvalue decompositions of A and B and the right...
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: PAMM
سال: 2013
ISSN: 1617-7061
DOI: 10.1002/pamm.201310273