Efficient variants of the CMRH method for solving a sequence of multi-shifted non-Hermitian linear systems simultaneouslyGu, X-M., Huang, T-Z., Carpentieri, B., Imakura, A., Zhang, K. & Du, L., Sep-2020, In : Journal of Computational and Applied Mathematics. 375, 16 p., 112788.
Research output: Contribution to journal › Article › Academic › peer-review
Multi-shifted linear systems with non-Hermitian coefficient matrices arise in numerical solutions of time-dependent partial/fractional differential equations (PDEs/FDEs), in control theory, PageRank problems, and other research fields. We derive efficient variants of the restarted Changing Minimal Residual method based on the cost-effective Hessenberg procedure (CMRH) for this problem class. Then, we introduce a flexible variant of the algorithm that allows to use variable preconditioning at each iteration to further accelerate the convergence of shifted CMRH. We analyse the performance of the new class of methods in the numerical solution of PDEs and FDEs, also against other multi-shifted Krylov subspace methods. (C) 2020 Elsevier B.V. All rights reserved.
|Number of pages||16|
|Journal||Journal of Computational and Applied Mathematics|
|Publication status||Published - Sep-2020|
- Krylov subspace methods, Shifted linear systems, Hessenberg procedure, GMRES, Shifted CMRH methods, FDEs, FULL ORTHOGONALIZATION METHOD, RESTARTED GMRES, KRYLOV METHODS, Q-OR, ALGORITHM, IMPLEMENTATION, CONVERGENCE, FAMILIES, BICG