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Publication Information
Title Extending the eigCG algorithm to nonsymmetric Lanczos for linear systems with multiple right-hand sides
Abstract 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 restar
Author(s) Konstantinos Orginos, Abdou Abdel-Rehim, Andreas Stathopoulos
Publication Date August 2014
Document Type Journal Article
Primary Institution The College of William and Mary, Williamsburg, VA
Affiliation Theory & Comp Physics / THEORY CENTER / THEORY CENTER
Funding Source
Proprietary? No
This publication conveys Technical Science Results
Document Numbers
JLAB Number: JLAB-THY-13-1724 OSTI Number: 1156889
LANL Number: arXiv:1302.4077 Other Number: DOE/OR/23177-2755
Associated with an experiment No
Associated with EIC No
Supported by Jefferson Lab LDRD Funding No
Journal Article
Journal Name Numerical Linear Algebra with Applications
Refereed Yes
Volume 21
Issue
Page(s) 473-493
Attachments/Datasets/DOI Link
Document(s)
1302.4077v1.pdf (STI Document)
DOI Link
Dataset(s) (none)
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