Extending the eigCG algorithm to nonsymmetric Lanczos for linear systems with multiple right-hand sides
The technique that was used to build the EigCG algorithm for sparse symmetric linear systems is extended to the nonsymmetric case using the BiCG algorithm. We show that, similarly to the symmetric case, we can build an algorithm that is capable of computing a few smallest magnitude eigenvalues and their corresponding left and right eigenvectors of a nonsymmetric matrix using only a small window of the BiCG residuals while simultaneously solving a linear system with that matrix. For a system with multiple right-hand sides, we give an algorithm that computes incrementally more eigenvalues while solving the first few systems and then uses the computed eigenvectors to deflate BiCGStab for the remaining systems. Our experiments on various test problems, including Lattice QCD, show the remarkable ability of EigBiCG to compute spectral approximations with accuracy comparable to that of the unrestarted, nonsymmetric Lanczos. Furthermore, our incremental EigBiCG followed by appropriately restarted and deflated BiCGStab provides a competitive method for systems with multiple right-hand sides.
- Research Organization:
- Thomas Jefferson National Accelerator Facility, Newport News, VA (United States)
- Sponsoring Organization:
- USDOE Office of Science (SC), Nuclear Physics (NP) (SC-26)
- DOE Contract Number:
- AC05-06OR23177
- OSTI ID:
- 1156889
- Report Number(s):
- JLAB-THY-13-1724; DOE/OR/23177-2755; arXiv:1302.4077; FC02-12ER41890; NSF CCF-0728915; Jeffress Memorial Trust grant J-813
- Journal Information:
- Numerical Linear Algebra with Applications, Journal Name: Numerical Linear Algebra with Applications Journal Issue: 4 Vol. 21; ISSN 1070-5325
- Country of Publication:
- United States
- Language:
- English
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