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The non-symmetric s-step Lanczos algorithm: Derivation of efficient recurrences and synchronization-reducing variants of BICG and QMR

Stefan FeuerriegelH. Martin Bücker — 2015

International Journal of Applied Mathematics and Computer Science

The Lanczos algorithm is among the most frequently used iterative techniques for computing a few dominant eigenvalues of a large sparse non-symmetric matrix. At the same time, it serves as a building block within biconjugate gradient (BiCG) and quasi-minimal residual (QMR) methods for solving large sparse non-symmetric systems of linear equations. It is well known that, when implemented on distributed-memory computers with a huge number of processes, the synchronization time spent on computing dot...

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