Geodesic
Simpler block GMRES for nonsymmetric systems with multiple right-hand sides
Electronic transactions on numerical analysis, Tome 30 (2008), pp. 1-9
A Simpler Block GMRES algorithm is presented, which is a block version of Walker and Zhou's Simpler GMRES. Similar to Block GMRES, the new algorithm also minimizes the residual norm in a block Krylov space at every step. Theoretical analysis shows that the matrix-valued polynomials constructed by the new algorithm is the same as the original one. However, Simpler Block GMRES avoids the factorization of a block upper Hessenberg matrix. In consequence, it is much simpler to program and requires less work. Numerical experiments are conducted to illustrate the performance of the new block algorithm.
Classification : 65F10
Keywords: linear systems, iterative methods, block methods, GMRES, simpler GMRES 
@article{ETNA_2008__30__a24,
     author = {Liu,  Hualei and Zhong,  Baojiang},
     title = {Simpler block {GMRES} for nonsymmetric systems with multiple right-hand sides},
     journal = {Electronic transactions on numerical analysis},
     pages = {1--9},
     year = {2008},
     volume = {30},
     zbl = {1188.65034},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2008__30__a24/}
}
TY  - JOUR
AU  - Liu,  Hualei
AU  - Zhong,  Baojiang
TI  - Simpler block GMRES for nonsymmetric systems with multiple right-hand sides
JO  - Electronic transactions on numerical analysis
PY  - 2008
SP  - 1
EP  - 9
VL  - 30
UR  - http://geodesic.mathdoc.fr/item/ETNA_2008__30__a24/
LA  - en
ID  - ETNA_2008__30__a24
ER  - 
%0 Journal Article
%A Liu,  Hualei
%A Zhong,  Baojiang
%T Simpler block GMRES for nonsymmetric systems with multiple right-hand sides
%J Electronic transactions on numerical analysis
%D 2008
%P 1-9
%V 30
%U http://geodesic.mathdoc.fr/item/ETNA_2008__30__a24/
%G en
%F ETNA_2008__30__a24
Liu,  Hualei; Zhong,  Baojiang. Simpler block GMRES for nonsymmetric systems with multiple right-hand sides. Electronic transactions on numerical analysis, Tome 30 (2008), pp. 1-9. http://geodesic.mathdoc.fr/item/ETNA_2008__30__a24/