most citedStructure of the polynomials in preconditioned BiCG algorithms and the switching direction of preconditioned systems

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math.NA2016★ 1 cited

Structure of the preconditioned system in various preconditioned conjugate gradient squared algorithms

Shoji Itoh, Masaaki Sugihara

An improved preconditioned conjugate gradient squared (PCGS) algorithm has recently been proposed, and it performs much better than the conventional PCGS algorithm. In this paper,…

math.NA2016★ 2 cited

Structure of the polynomials in preconditioned BiCG algorithms and the switching direction of preconditioned systems

Shoji Itoh, Masaaki Sugihara

We present a theorem that defines the direction of a preconditioned system for the bi-conjugate gradient (BiCG) method, and we extend it to preconditioned bi-Lanczos-type algorithm…