Geodesic
Derivation of BiCG from the conditions defining Lanczos' method for solving a system of linear equations
Applications of Mathematics, Tome 43 (1998) no. 5, pp. 381-388.

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Lanczos’ method for solving the system of linear algebraic equations $Ax=b$ consists in constructing a sequence of vectors $x_k$ in such a way that $r_k=b-Ax_k \in r_0+A{\mathcal K}_{k}(A,r_0)$ and $r_k \perp {\mathcal K}_{k}(A^T,\widetilde{r}_0)$. 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.
DOI : 10.1023/A:1022238402573
Classification : 65F10, 65F25
Keywords: biorthogonalization; linear equations; biconjugate gradient method 
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     title = {Derivation of {BiCG} from the conditions defining {Lanczos'} method for solving a system of linear equations},
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Tichý, Petr; Zítko, Jan. Derivation of BiCG from the conditions defining Lanczos' method for solving a system of linear equations. Applications of Mathematics, Tome 43 (1998) no. 5, pp. 381-388. doi : 10.1023/A:1022238402573. http://geodesic.mathdoc.fr/articles/10.1023/A:1022238402573/

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