Deflated Iterative Methods for Linear Equations with Multiple Right-Hand Sides

Abstract

A new approach is discussed for solving large nonsymmetric systems of linear equations with multiple right-hand sides. The first system is solved with a deflated GMRES method that generates eigenvector information at the same time that the linear equations are solved. Subsequent systems are solved by combining an iterative method with a projection over the previously determined eigenvectors. Restarted GMRES is considered for the iterative method as well as non-restarted methods such as BiCGSTAB. These methods offer an alternative to block methods, and they can also be combined with a block approach. An example is given showing significant improvement for a problem from quantum chromodynamics.

28 pages, 9 figures; support acknowledgments added

References in corpus (5)

• A study of chiral symmetry in quenched QCD using the Overlap-Dirac operator
• On the low fermionic eigenmode dominance in QCD on the lattice
• Chiral Symmetry, Quark Mass, and Scaling of the Overlap Fermions
• Progress on lattice QCD algorithms
• Linear systems solvers - recent developments and implications for lattice computations

Cited by in corpus (12)

• Effective noise reduction techniques for disconnected loops in Lattice QCD
• Computing and deflating eigenvalues while solving multiple right hand side linear systems in Quantum Chromodynamics
• Deflated GMRES for Systems with Multiple Shifts and Multiple Right-Hand Sides
• Deflation as a Method of Variance Reduction for Estimating the Trace of a Matrix Inverse
• Application of block Krylov subspace algorithms to the Wilson-Dirac equation with multiple right-hand sides in lattice QCD
• An iterative method to compute the overlap Dirac operator at nonzero chemical potential
• Extending the eigCG algorithm to nonsymmetric Lanczos for linear systems with multiple right-hand sides
• Application of preconditioned block BiCGGR to the Wilson-Dirac equation with multiple right-hand sides in lattice QCD
• An iterative method to compute the sign function of a non-Hermitian matrix and its application to the overlap Dirac operator at nonzero chemical potential
• Deflated GMRES with Multigrid for Lattice QCD
• Deflated Hermitian Lanczos Methods for Multiple Right-Hand Sides
• Two-Grid Deflated Krylov Methods for Linear Equations