Restarted GMRES for Shifted Linear Systems
SIAM Journal on Scientific Computing
Extended Krylov Subspaces: Approximation of the Matrix Square Root and Related Functions
SIAM Journal on Matrix Analysis and Applications
The Solution of Parametrized Symmetric Linear Systems
SIAM Journal on Matrix Analysis and Applications
Approximation of Large-Scale Dynamical Systems (Advances in Design and Control) (Advances in Design and Control)
A New Iterative Method for Solving Large-Scale Lyapunov Matrix Equations
SIAM Journal on Scientific Computing
Stopping Criteria for Rational Matrix Functions of Hermitian and Symmetric Matrices
SIAM Journal on Scientific Computing
Computing $A^\alpha, \log(A)$, and Related Matrix Functions by Contour Integrals
SIAM Journal on Numerical Analysis
Low-Rank Tensor Krylov Subspace Methods for Parametrized Linear Systems
SIAM Journal on Matrix Analysis and Applications
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The Extended Krylov subspace has recently received considerable attention as a powerful tool for matrix function evaluations and other problems involving large matrices. In this paper we show that this space has a great potential within projection-type methods for effectively solving several other important large-scale algebraic problems: we focus on the solution of shifted systems and of more general parameter-dependent matrix equations, and on the approximation of the transfer function by projection. Numerical experiments stemming from real applications show the effectiveness of the approach.