GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems
SIAM Journal on Scientific and Statistical Computing
The numerical analysis of ordinary differential equations: Runge-Kutta and general linear methods
The numerical analysis of ordinary differential equations: Runge-Kutta and general linear methods
A characterization of all solutions to the four block general distance problem
SIAM Journal on Control and Optimization
Parallel diagonally implicit Runge-Kutta-Nystro¨m methods
Applied Numerical Mathematics
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Diagonally-implicit multi-stage integration methods
Applied Numerical Mathematics
Using Krylov methods in the solution of large-scale differential-algebraic systems
SIAM Journal on Scientific Computing
Application of ADI Iterative Methods to the Restoration of Noisy Images
SIAM Journal on Matrix Analysis and Applications
Mono-implicit Runge-Kutta schemes for the parallel solution of initial value ODEs
Journal of Computational and Applied Mathematics
Augmented Lagrange-SQP Methods with Lipschitz-Continuous Lagrange Multiplier Updates
SIAM Journal on Numerical Analysis
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
Krylov subspace methods for large-scale matrix problems in control
Future Generation Computer Systems - Selected papers on theoretical and computational aspects of structural dynamical systems in linear algebra and control
Sylvester Tikhonov-regularization methods in image restoration
Journal of Computational and Applied Mathematics
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The Runge-Kutta method is one of the most popular implicit methods for the solution of stiff ordinary differential equations. For large problems, the main drawback of such methods is the cost required at each integration step for computing the solution of a nonlinear system of equations. In this paper, we propose to reduce the cost of the computation by transforming the linear systems arising in the application of Newton's method to Stein matrix equations. We propose an iterative projection method onto block Krylov subspaces for solving numerically such Stein matrix equations. Numerical examples are given to illustrate the performance of our proposed method.