Restarted GMRES for Shifted Linear Systems
- A. Frommer, U. Glässner
- Computer Science, MathematicsSIAM Journal on Scientific Computing
- 1998
This work develops a variant of the restarted GMRES method exhibiting the same advantage and investigates its convergence for positive real matrices in some detail and applies it to speed up "multiple masses" calculations arising in lattice gauge computations in quantum chromodynamics, one of the most time-consuming supercomputer applications.
H-Splittings and two-stage iterative methods
- A. Frommer, D. Szyld
- Mathematics
- 1 December 1992
SummaryConvergence of two-stage iterative methods for the solution of linear systems is studied. Convergence of the non-stationary method is shown if the number of inner iterations becomes…
BiCGStab(ℓ) for Families of Shifted Linear Systems
- A. Frommer
- MathematicsComputing
- 1 April 2003
Modifications of the BiCGStab(ℓ) method are developed which allow to solve the seed and the shifted system at the expense of just the matrix-vector multiplications needed to solve Ax = b via BiCGstab( ℓ), showing that in the case that A is positive real and σ ≥ 0, the resulting method is still a well-smoothed variant of BiCG.
Fast CG-Based Methods for Tikhonov-Phillips Regularization
- A. Frommer, P. Maass
- MathematicsSIAM Journal on Scientific Computing
- 1 April 1999
Two methods for accelerating the standard cg-algorithm for solving the family of systems (* using the shifted structure of the linear systems and a stopping criterion which depends on $\alpha$ and $\delta$ are investigated.
Convergence of relaxed parallel multisplitting methods
- A. Frommer, G. Mayer
- Computer Science, Mathematics
- 1 July 1989
Asynchronous Iterations
- A. Frommer, D. Szyld
- Mathematics, Computer ScienceEncyclopedia of Parallel Computing
- 2011
Certain models of asynchronous iterations, using a common theoretical framework, are reviewed, including nonsingular linear systems, nonlinear systems, and initial value problems that arise naturally on parallel computers.
Numerical methods for the QCDd overlap operator. I. Sign-function and error bounds
- J. D. Eshof, A. Frommer, T. Lippert, K. Schilling, H. A. Vorst
- Computer Science, Mathematics
- 25 February 2002
Efficient schemes for nearest neighbor load balancing
- R. Diekmann, A. Frommer, B. Monien
- Computer ScienceParallel Computing
- 1 July 1999
On asynchronous iterations
- A. Frommer, D. Szyld
- Computer Science, Mathematics
- 1 November 2000
Weighted max norms, splittings, and overlapping additive Schwarz iterations
- A. Frommer, D. Szyld
- Computer ScienceNumerische Mathematik
- 1 August 1999
Weighted max-norm bounds are obtained for Algebraic Additive Schwarz Iterations with overlapping blocks for the solution of Ax = b, when the coefficient matrix A is an M-matrix and a new theorem concerning P-regular splittings is presented which provides a useful tool for the A- norm bounds.
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