Title page for ETD etd-08252009-161256

Type of Document Master's Thesis
Author Ahuja, Kapil
Author's Email Address kahuja@vt.edu
URN etd-08252009-161256
Title Recycling Bi-Lanczos Algorithms: BiCG, CGS, and BiCGSTAB
Degree Master of Science
Department Mathematics
Advisory Committee
Advisor Name Title
de Sturler, Eric Committee Chair
Beattie, Christopher A. Committee Member
Borggaard, Jeffrey T. Committee Member
Gugercin, Serkan Committee Member
  • Krylov subspace recycling
  • Petrov-Galerkin formulation
  • bi-Lanczos method
Date of Defense 2009-08-13
Availability unrestricted
Engineering problems frequently require solving a sequence of dual linear systems. This paper introduces recycling BiCG, that recycles the Krylov subspace from one pair of linear systems to the next pair. Augmented bi-Lanczos algorithm and modified two-term recurrence are developed for using the recycle space. Recycle space is built from the approximate invariant subspace corresponding to eigenvalues close to the origin. Recycling approach is extended to the CGS and the BiCGSTAB algorithms. Experiments on a convection-diffusion problem give promising results.
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