1 research outputs found
Recycling BiCG for families of shifted linear systems
Many problems in science and engineering fields require the solution of
shifted linear systems. To solve such systems efficiently, the recycling BiCG
(RBiCG) algorithm in [SIAM J. SCI. COMPUT, 34 (2012) 1925-1949] is extended in
this paper. However, the shift-invariant property could no longer hold over the
augmented Krylov subspace due to adding the recycling spaces. To remedy this
situation, a strategy to enforce the collinearity condition on the shifted
system is adopted and then a short term recurrence for the solution update of
the shifted system is derived when the seed system is solving. The new method
not only improves the convergence but also has a potential to simultaneously
compute approximate solutions for shifted linear systems using only as many
matrix-vector multiplications as the solution of a single system requires. In
addition, some numerical experiments also confirm the efficiency of our method.Comment: This paper has been withdrawn by the author due to a crucial sign
error in articl