An element-by-element solution algorithm for nonsymmetric linear systems of equations

1990 ◽  
pp. 295-304 ◽  
Author(s):  
M. B. van Gijzen ◽  
P. Nauta
Keyword(s):  
Linear Systems ◽  
Solution Algorithm ◽  
Element Solution ◽  
Systems Of Equations ◽  
Nonsymmetric Linear Systems ◽  
Linear Systems Of Equations

scholarly journals Lanczos-type solvers for nonsymmetric linear systems of equations

Acta Numerica ◽  
1997 ◽  
Vol 6 ◽  
pp. 271-397 ◽  
Author(s):  
Martin H. Gutknecht
Keyword(s):  
Linear Systems ◽  
Low Cost ◽  
Systems Of Equations ◽  
Nonsymmetric Linear Systems ◽  
Lanczos Process ◽  
Krylov Space ◽  
Look Ahead ◽  
Nonsymmetric Matrix ◽  
Large Linear Systems ◽  
Linear Systems Of Equations

Among the iterative methods for solving large linear systems with a sparse (or, possibly, structured) nonsymmetric matrix, those that are based on the Lanczos process feature short recurrences for the generation of the Krylov space. This means low cost and low memory requirement. This review article introduces the reader not only to the basic forms of the Lanczos process and some of the related theory, but also describes in detail a number of solvers that are based on it, including those that are considered to be the most efficient ones. Possible breakdowns of the algorithms and ways to cure them by look-ahead are also discussed.

Solving Non-linear Systems of Equations on Graphics Processing Units

2010 ◽  
pp. 719-729 ◽  
Author(s):  
Lubomir T. Dechevsky ◽  
Børre Bang ◽  
Joakim Gundersen ◽  
Arne Lakså ◽  
Arnt R. Kristoffersen
Keyword(s):  
Linear Systems ◽  
Graphics Processing Units ◽  
Systems Of Equations ◽  
Non Linear ◽  
Non Linear Systems ◽  
Graphics Processing ◽  
Linear Systems Of Equations

Linear Systems of Equations

1993 ◽  
pp. 175-194
Author(s):  
Ulrich Kulisch ◽  
Rolf Hammer ◽  
Dietmar Ratz ◽  
Matthias Hocks
Keyword(s):  
Linear Systems ◽  
Systems Of Equations ◽  
Linear Systems Of Equations
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