Physics – Mathematical Physics
Scientific paper
2007-07-03
LinearAlgebraAppl.429:2415-2434,2008
Physics
Mathematical Physics
19 pages, 9 figures
Scientific paper
10.1016/j.laa.2008.04.019
We consider solution of multiply shifted systems of nonsymmetric linear equations, possibly also with multiple right-hand sides. First, for a single right-hand side, the matrix is shifted by several multiples of the identity. Such problems arise in a number of applications, including lattice quantum chromodynamics where the matrices are complex and non-Hermitian. Some Krylov iterative methods such as GMRES and BiCGStab have been used to solve multiply shifted systems for about the cost of solving just one system. Restarted GMRES can be improved by deflating eigenvalues for matrices that have a few small eigenvalues. We show that a particular deflated method, GMRES-DR, can be applied to multiply shifted systems. In quantum chromodynamics, it is common to have multiple right-hand sides with multiple shifts for each right-hand side. We develop a method that efficiently solves the multiple right-hand sides by using a deflated version of GMRES and yet keeps costs for all of the multiply shifted systems close to those for one shift. An example is given showing this can be extremely effective with a quantum chromodynamics matrix.
Darnell Dean
Morgan Ronald B.
Wilcox Walter
No associations
LandOfFree
Deflated GMRES for Systems with Multiple Shifts and Multiple Right-Hand Sides does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Deflated GMRES for Systems with Multiple Shifts and Multiple Right-Hand Sides, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Deflated GMRES for Systems with Multiple Shifts and Multiple Right-Hand Sides will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-546519