Abstract
In many relevant large scale computations one has to solve very large linear nonsymmetric systems. Often there is no alternative but to solve these systems by some iterative solution method. In the past few years new methods have emerged that can be seen as combinations of standard Krylov subspace methods, such as Bi-CG and GMRES. One of the first hybrid schemes of this type is CGS, actually the Bi-CG squared method. Other such hybrid schemes include BiCGSTAB (a combination of Bi-CG and GMRES(1)), BiCGSTAB(ℓ) (Bi-CG combined with GMRES(ℓ)), and the nested GMRESR method (GMRES preconditioned by itself or other schemes). These methods have been successful in solving relevant sparse nonsymmetric linear systems.
After a presentation of some recent methods we will discuss briefly implementation issues of the Krylov subspace methods, including possibilities for distributed parallel computation.
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Van der Vorst, H.A. (1994). Recent developments in hybrid CG methods. In: Gentzsch, W., Harms, U. (eds) High-Performance Computing and Networking. HPCN-Europe 1994. Lecture Notes in Computer Science, vol 797. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-57981-8_113
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DOI: https://doi.org/10.1007/3-540-57981-8_113
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