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Mathematics > Numerical Analysis

arXiv:1403.3876 (math)
This paper has been withdrawn by Jing Meng Doctor
[Submitted on 16 Mar 2014 (v1), last revised 25 Jun 2014 (this version, v2)]

Title:Recycling BiCG for families of shifted linear systems

Authors:Jing Meng, Pei-yong Zhu, Hou-Biao Li
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Abstract: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.
Comments: This paper has been withdrawn by the author due to a crucial sign error in article
Subjects: Numerical Analysis (math.NA)
MSC classes: 65F10
ACM classes: G.1.3
Cite as: arXiv:1403.3876 [math.NA]
  (or arXiv:1403.3876v2 [math.NA] for this version)
  https://doi.org/10.48550/arXiv.1403.3876

Submission history

From: Jing Meng Doctor [view email]
[v1] Sun, 16 Mar 2014 03:21:58 UTC (149 KB)
[v2] Wed, 25 Jun 2014 13:07:04 UTC (1 KB) (withdrawn)
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