Geodesic
An algorithm of the simplex method using a~dual basis
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 18 (2015) no. 4, pp. 349-359

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An algorithm of the simplex method not requiring an explicit updating of the $LU$ decomposition in iterations is considered. Solutions obtained with fixed $LU$ factors are corrected using small auxiliary matrices. The results of numerical experiments are presented. 
@article{SJVM_2015_18_4_a0,
     author = {G. I. Zabinyako},
     title = {An algorithm of the simplex method using a~dual basis},
     journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
     pages = {349--359},
     publisher = {mathdoc},
     volume = {18},
     number = {4},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJVM_2015_18_4_a0/}
}
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G. I. Zabinyako. An algorithm of the simplex method using a~dual basis. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 18 (2015) no. 4, pp. 349-359. http://geodesic.mathdoc.fr/item/SJVM_2015_18_4_a0/