Application of ADI Iterative Methods to the Restoration of Noisy Images
SIAM Journal on Matrix Analysis and Applications
Matrix computations (3rd ed.)
The Chebyshev Polynomials of a Matrix
SIAM Journal on Matrix Analysis and Applications
ACM Transactions on Mathematical Software (TOMS)
Superlinear Convergence of Conjugate Gradients
SIAM Journal on Numerical Analysis
Approximation of Large-Scale Dynamical Systems (Advances in Design and Control) (Advances in Design and Control)
Gramian-Based Model Reduction for Data-Sparse Systems
SIAM Journal on Scientific Computing
$\mathcal{H}_2$ Model Reduction for Large-Scale Linear Dynamical Systems
SIAM Journal on Matrix Analysis and Applications
On the ADI method for Sylvester equations
Journal of Computational and Applied Mathematics
Convergence Analysis of Projection Methods for the Numerical Solution of Large Lyapunov Equations
SIAM Journal on Numerical Analysis
Solution of Large Scale Evolutionary Problems Using Rational Krylov Subspaces with Optimized Shifts
SIAM Journal on Scientific Computing
Error Estimates and Evaluation of Matrix Functions via the Faber Transform
SIAM Journal on Numerical Analysis
Krylov Subspace Methods for Linear Systems with Tensor Product Structure
SIAM Journal on Matrix Analysis and Applications
On the Convergence of Rational Ritz Values
SIAM Journal on Matrix Analysis and Applications
Convergence analysis of the extended Krylov subspace method for the Lyapunov equation
Numerische Mathematik
Analysis of the Rational Krylov Subspace and ADI Methods for Solving the Lyapunov Equation
SIAM Journal on Numerical Analysis
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In this paper we suggest a new formula for the residual of Galerkin projection onto rational Krylov spaces applied to a Sylvester equation, and establish a relation to three different underlying extremal problems for rational functions. These extremal problems enable us to compare the size of the residual for the above method with that obtained by ADI. In addition, we deduce several new a priori error estimates for Galerkin projection onto rational Krylov spaces, both for the Sylvester and for the Lyapunov equation.