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Showing 1 to 5 of 5 for “"BiCG"”.
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Analysis of the BiCG Method
The Biconjugate Gradient (BiCG) method is an iterative Krylov subspace method that utilizes a 3-term recurrence. BiCG is the basis of several very popular methods, such as BiCGStab. The short recurrence makes BiCG preferable to other Krylov methods because of decreased memory usage and CPU time. …
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Recycling Bi-Lanczos Algorithms: BiCG, CGS, and BiCGSTAB
… 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 …
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Recycling Krylov Subspaces and Preconditioners
… Lanczos vectors, using BiConjugate Gradients (BiCG) to solve dual linear systems may have application-specific advantages. For example, using BiCG to solve the dual linear systems arising in interpolatory model reduction provides a backward error formulation in the model reduction framework. …
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Inexact Solves in Interpolatory Model Reduction
… the stopping tolerances, employing GMRES and BiCG as the inexact solvers, and using different initial shift selections. For just one step of Krylov reduction, we verified theoretical properties of the interpolation error. Also, we found a linear improvement in the subspace angles between the …
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Distributed analysis of Markov chains
… chains are surveyed and two iterative methods, BiCG and BiCGSTAB, were chosen for a parallel implementation to show that this stage of analysis also benefits from a distributed approach. The results from the distributed generation algorithm show a good speed up of the state space generation phase …