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arXiv · 1403.3876

Recycling BiCG for families of shifted linear systems

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.

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Jing Meng, Pei-yong Zhu, Hou-Biao Li. 2014-06-25. Recycling BiCG for families of shifted linear systems. https://arxiv.org/abs/1403.3876

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