The Cycle-Convergence of Restarted GMRES for Normal Matrices Is Sublinear

The Cycle-Convergence of Restarted GMRES for Normal Matrices Is Sublinear

We prove that the cycle–convergence of the restarted GMRES applied to a system of linear equations with a normal coefficient matrix is sublinear.

Morning Session I the Convergence of Restarted Gmres for Normal Matrices

Breakfast and Registration: 8:30 9:00 Morning Session I Room 1312 9:00 11:00 9:00 9:20 Eugene Vecharynski The Convergence of Restarted GMRES University of Colorado at Denver for Normal Matrices is Sublinear 9:25 9:45 Adrianna Gillman The Numerical Performace of a Mixed-Hybrid University of Colorado at Boulder Type Solution Methodology for Solving High-Frequency Helmholtz Problems 9:50 10:10 Sri...

Any admissible cycle-convergence behavior is possible for restarted GMRES at its initial cycles

We show that any admissible cycle-convergence behavior is possible for restarted GMRES at a number of initial cycles, moreover the spectrum of the coefficient matrix alone does not determine this cycleconvergence. The latter can be viewed as an extension of the result of Greenbaum, Pták and Strakoš (SIAM Journal on Matrix Analysis and Applications 1996; 17(3):465–469) to the case of restarted G...

A Technique for Accelerating the Convergence of Restarted GMRES

On the Admissible Convergence Curves for Restarted Gmres

Abstract. This paper studies admissible convergence curves for restarted GMRES and their relation to the curves for full GMRES. It shows that stagnation at the end of a restart cycle is mirrored at the beginning of the next cycle. Otherwise, any non-increasing convergence curve is possible and pairs {A, b} are constructed such that when restarted GMRES is applied to Ax = b, prescribed residual ...