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Derivation of BiCG from the conditions defining Lanczos' method for solving a system of linear equations

Petr Tichý; Jan Zítko — 1998

Applications of Mathematics

Lanczos’ method for solving the system of linear algebraic equations $A x = b$ consists in constructing a sequence of vectors $x_{k}$ in such a way that $r_{k} = b - A x_{k} \in r_{0} + A 𝒦_{k} (A, r_{0})$ and $r_{k} ⊥ 𝒦_{k} (A^{T}, {\tilde{r}}_{0})$ . This sequence of vectors can be computed by the BiCG (BiOMin) algorithm. In this paper is shown how to obtain the recurrences of BiCG (BiOMin) directly from this conditions.

Editorial

Stanislav Sysala; Petr Tichý — 2022

Applications of Mathematics

Editorial

Stanislav Sysala; Petr Tichý — 2020

Applications of Mathematics

On the worst-case convergence of MR and CG for symmetric positive definite tridiagonal Toeplitz matrices.

Liesen, Jörg; Tichý, Petr — 2005

ETNA. Electronic Transactions on Numerical Analysis [electronic only]

On error estimation in the conjugate gradient method and why it works in finite precision computations.

Strakoš, Zdeněk; Tichý, Petr — 2002

ETNA. Electronic Transactions on Numerical Analysis [electronic only]

On worst-case GMRES, ideal GMRES, and the polynomial numerical hull of a Jordan block.

Tichý, Petr; Liesen, Jörg; Faber, Vance — 2007

ETNA. Electronic Transactions on Numerical Analysis [electronic only]

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Currently displaying 1 – 6 of 6

Derivation of BiCG from the conditions defining Lanczos' method for solving a system of linear equations

Editorial

Editorial

On the worst-case convergence of MR and CG for symmetric positive definite tridiagonal Toeplitz matrices.

On error estimation in the conjugate gradient method and why it works in finite precision computations.

On worst-case GMRES, ideal GMRES, and the polynomial numerical hull of a Jordan block.