Multipreconditioned GMRES for Shifted Systems

• Main Authors: Bakhos, Tania, Kitanidis, Peter, Ladenheim, Scott, Saibaba, Arvind K, Szyld, Daniel
• Format: Journal Article
• Language: English
• Published: 29-03-2016
• Subjects: Mathematics - Numerical Analysis
• DOI: 10.48550/arxiv.1603.08970

An implementation of GMRES with multiple preconditioners (MPGMRES) is
proposed for solving shifted linear systems with shift-and-invert
preconditioners. With this type of preconditioner, the Krylov subspace can be
built without requiring the matrix-vector product with the shifted matrix.
Furthermore, the multipreconditioned search space is shown to grow only
linearly with the number of preconditioners. This allows for a more efficient
implementation of the algorithm. The proposed implementation is tested on
shifted systems that arise in computational hydrology and the evaluation of
different matrix functions. The numerical results indicate the effectiveness of
the proposed approach.