Geodesic
On modification of certain methods of the conjugate direction type for solving rectangular systems of linear algebraic equations
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 47 (2007) no. 12, pp. 1979-1987

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The use of modifications of certain well-known methods of the conjugate direction type for solving systems of linear algebraic equations with rectangular matrices is examined. The modified methods are shown to be superior to the original versions with respect to the round-off accumulation; the advantage is especially large for ill-conditioned matrices. Examples are given of the efficient use of the modified methods for solving certain fairly large ill-conditioned problems. 
@article{ZVMMF_2007_47_12_a1,
     author = {L. F. Yukhno},
     title = {On modification of certain methods of the conjugate direction type for solving rectangular systems of linear algebraic equations},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1979--1987},
     publisher = {mathdoc},
     volume = {47},
     number = {12},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2007_47_12_a1/}
}
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L. F. Yukhno. On modification of certain methods of the conjugate direction type for solving rectangular systems of linear algebraic equations. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 47 (2007) no. 12, pp. 1979-1987. http://geodesic.mathdoc.fr/item/ZVMMF_2007_47_12_a1/