Geodesic
Oblique projection methods for linear systems with multiple right-hand sides
Electronic transactions on numerical analysis, Tome 20 (2005), pp. 119-138
In the present paper, we describe new Lanczos-based methods for solving nonsymmetric linear systems of equations with multiple right-hand sides. These methods are based on global oblique projections of the initial residual onto a matrix Krylov subspace. We first derive the global Lanczos process to construct biorthonormal bases and we give some of its properties. Then we introduce new methods such as the global BCG and the global BiCGSTAB algorithms. Look-ahead versions of these algorithms are also given. Finally numerical examples will be given.
Classification : 65F10, 65F25
Keywords: global Lanczos, matrix Krylov subspace, block methods, iterative methods, nonsymmetric linear systems, multiple right-hand sides 
@article{ETNA_2005__20__a8,
     author = {Jbilou,  K. and Sadok,  H. and Tinzefte,  A.},
     title = {Oblique projection methods for linear systems with multiple right-hand sides},
     journal = {Electronic transactions on numerical analysis},
     pages = {119--138},
     year = {2005},
     volume = {20},
     zbl = {1121.65313},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2005__20__a8/}
}
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%A Tinzefte,  A.
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%J Electronic transactions on numerical analysis
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Jbilou,  K.; Sadok,  H.; Tinzefte,  A. Oblique projection methods for linear systems with multiple right-hand sides. Electronic transactions on numerical analysis, Tome 20 (2005), pp. 119-138. http://geodesic.mathdoc.fr/item/ETNA_2005__20__a8/