Journal of Computational Physics
Interpreting IDR as a Petrov-Galerkin Method
SIAM Journal on Scientific Computing
On Adaptive Choice of Shifts in Rational Krylov Subspace Reduction of Evolutionary Problems
SIAM Journal on Scientific Computing
Analysis of the Rational Krylov Subspace and ADI Methods for Solving the Lyapunov Equation
SIAM Journal on Numerical Analysis
On the Convergence of Krylov Subspace Methods for Matrix Mittag-Leffler Functions
SIAM Journal on Numerical Analysis
A rational Arnoldi approach for ill-conditioned linear systems
Journal of Computational and Applied Mathematics
On the generation of Krylov subspace bases
Applied Numerical Mathematics
An Error Analysis for Rational Galerkin Projection Applied to the Sylvester Equation
SIAM Journal on Numerical Analysis
Using the Restricted-denominator Rational Arnoldi Method for Exponential Integrators
SIAM Journal on Matrix Analysis and Applications
Computation of matrix functions with deflated restarting
Journal of Computational and Applied Mathematics
Preconditioning linear systems via matrix function evaluation
Applied Numerical Mathematics
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The need to evaluate expressions of the form $f(A)$ or $f(A)b$, where $f$ is a nonlinear function, $A$ is a large sparse $n\times n$ matrix, and $b$ is an $n$-vector, arises in many applications. This paper describes how the Faber transform applied to the field of values of $A$ can be used to determine improved error bounds for popular polynomial approximation methods based on the Arnoldi process. Applications of the Faber transform to rational approximation methods and, in particular, to the rational Arnoldi process also are discussed.