Derivation of BiCG from the conditions defining Lanczos' method for solving a system of linear equations
Applications of Mathematics (1998)
- Volume: 43, Issue: 5, page 381-388
- ISSN: 0862-7940
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topTichý, Petr, and Zítko, Jan. "Derivation of BiCG from the conditions defining Lanczos' method for solving a system of linear equations." Applications of Mathematics 43.5 (1998): 381-388. <http://eudml.org/doc/33016>.
@article{Tichý1998,
abstract = {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.},
author = {Tichý, Petr, Zítko, Jan},
journal = {Applications of Mathematics},
keywords = {biorthogonalization; linear equations; biconjugate gradient method; biorthogonalization; linear equations; biconjugate gradient method},
language = {eng},
number = {5},
pages = {381-388},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Derivation of BiCG from the conditions defining Lanczos' method for solving a system of linear equations},
url = {http://eudml.org/doc/33016},
volume = {43},
year = {1998},
}
TY - JOUR
AU - Tichý, Petr
AU - Zítko, Jan
TI - Derivation of BiCG from the conditions defining Lanczos' method for solving a system of linear equations
JO - Applications of Mathematics
PY - 1998
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 43
IS - 5
SP - 381
EP - 388
AB - 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.
LA - eng
KW - biorthogonalization; linear equations; biconjugate gradient method; biorthogonalization; linear equations; biconjugate gradient method
UR - http://eudml.org/doc/33016
ER -
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