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Showing 1 to 6 of 6 for “"Krylov subspace recycling"”.
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Strategies For Recycling Krylov Subspace Methods and Bilinear Form Estimation
… of this work is effectiveness and efficiency of Krylov subspace methods and Krylov subspace recycling. While solving long, slowly changing sequences of large linear systems, such as the ones that arise in engineering, there are many issues we need to consider if we want to make the process …
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Iterative Solution Methods for Reduced-Order Models of Parameterized Partial Differential Equations
… systems, either by reusing preconditioners or by recycling Krylov vectors. These two approaches are shown to be effective when the underlying PDE is linear. For nonlinear problems, we utilize the discrete empirical interpolation method (DEIM) to cheaply evaluate the nonlinear components of the …
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Krylov Subspace Methods with Fixed Memory Requirements: Nearly Hermitian Linear Systems and Subspace Recycling
Krylov subspace iterative methods provide an effective tool for reducing the solution of large linear systems to a size for which a direct solver may be applied. However, the problems of limited storage and speed are still a concern. Therefore, in this dissertation work, we present iterative Krylov …
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Recycling Techniques for Sequences of Linear Systems and Eigenproblems
… sequences of linear systems and eigenproblems. Recycling techniques, such as recycling preconditioners or subspaces, are popular approaches for reducing computational cost. In this thesis, we introduce two novel approaches for recycling previously computed information for a subsequent system or …
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Recycling Bi-Lanczos Algorithms: BiCG, CGS, and BiCGSTAB
… 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 …
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Recycling Krylov Subspaces and Preconditioners
… systems. We develop algorithms that recycle Krylov subspaces and preconditioners from one system (or pair of systems) in the sequence to the next, leading to efficient solutions. Besides the benefit of only having to store few Lanczos vectors, using BiConjugate Gradients (BiCG) to solve dual …