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    Krylov subspace recycling for sequences of shifted linear systems

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    Genre
    Journal Article
    Date
    2014-01-01
    Author
    Soodhalter, KM
    Szyld, DB
    Xue, F
    Subject
    Krylov subspace methods
    Subspace recycling
    Shifted linear systems
    QCD
    Permanent link to this record
    http://hdl.handle.net/20.500.12613/5915
    
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    DOI
    10.1016/j.apnum.2014.02.006
    Abstract
    We study the use of Krylov subspace recycling for the solution of a sequence of slowly-changing families of linear systems, where each family consists of shifted linear systems that differ in the coefficient matrix only by multiples of the identity. Our aim is to explore the simultaneous solution of each family of shifted systems within the framework of subspace recycling, using one augmented subspace to extract candidate solutions for all the shifted systems. The ideal method would use the same augmented subspace for all systems and have fixed storage requirements, independent of the number of shifted systems per family. We show that a method satisfying both requirements cannot exist in this framework. As an alternative, we introduce two schemes. One constructs a separate deflation space for each shifted system but solves each family of shifted systems simultaneously. The other builds only one recycled subspace and constructs approximate corrections to the solutions of the shifted systems at each cycle of the iterative linear solver while only minimizing the base system residual. At convergence of the base system solution, we apply the method recursively to the remaining unconverged systems. We present numerical examples involving systems arising in lattice quantum chromodynamics. © 2014 IMACS.
    Citation to related work
    Elsevier BV
    Has part
    Applied Numerical Mathematics
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    ae974a485f413a2113503eed53cd6c53
    http://dx.doi.org/10.34944/dspace/5897
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