A polynomial method based on Fejèr points for the computation of functions of unsymmetric matrices
Applied Numerical Mathematics
A Krylov Subspace Method for Covariance Approximation and Simulation of Random Processes and Fields
Multidimensional Systems and Signal Processing
The Gautschi time stepping scheme for edge finite element discretizations of the Maxwell equations
Journal of Computational Physics
A rational Krylov method for solving time-periodic differential equations
Applied Numerical Mathematics
Application of operator splitting to the Maxwell equations including a source term
Applied Numerical Mathematics
ICCS'03 Proceedings of the 2003 international conference on Computational science: PartIII
Extended Krylov subspace for parameter dependent systems
Applied Numerical Mathematics
Extended Arnoldi methods for large low-rank Sylvester matrix equations
Applied Numerical Mathematics
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
Block Arnoldi-based methods for large scale discrete-time algebraic Riccati equations
Journal of Computational and Applied Mathematics
Computing $f(A)b$ via Least Squares Polynomial Approximations
SIAM Journal on Scientific Computing
Analysis of the Rational Krylov Subspace and ADI Methods for Solving the Lyapunov 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
A fast multipole method for the Rotne-Prager-Yamakawa tensor and its applications
Journal of Computational Physics
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We introduce an economical Gram--Schmidt orthogonalization on the extended Krylov subspace originated by actions of a symmetric matrix and its inverse. An error bound for a family of problems arising from the elliptic method of lines is derived. The bound shows that, for the same approximation quality, the diagonal variant of the extended subspaces requires about the square root of the dimension of the standard Krylov subspaces using only positive or negative matrix powers. An example of an application to the solution of a 2.5-D elliptic problem attests to the computational efficiency of the method for large-scale problems.