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An improved lower bound on a positive stable block triangular preconditioner for saddle point problems. (English) Zbl 1252.65067

Summary: In this paper, a new lower bound on a positive stable block triangular preconditioner for saddle point problems is derived; it is superior to the corresponding result obtained by Z.-H. Cao [Appl. Numer. Math. 57, No. 8, 899–910 (2007; Zbl 1118.65021)]. A numerical example is reported to confirm the presented result.

MSC:

65F08 Preconditioners for iterative methods

Citations:

Zbl 1118.65021

Software:

IFISS
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References:

[1] Axelsson, O.; Barker, V.A., Finite element solution of boundary value problems, (1984), Academic Press Orlando · Zbl 0537.65072
[2] Brezzi, F.; Fortin, M., Mixed and hybrid finite element methods, (1991), Springer New York · Zbl 0788.73002
[3] Elman, H.C.; Silvester, D.J.; Wathen, A.J., Finite elements and fast iterative solvers, (2003), Oxford University Press Oxford
[4] Zulehner, W., Analysis of iterative methods for saddle point problems a unified approach, Math. comp., 71, 479-505, (2001) · Zbl 0996.65038
[5] Benzi, M.; Golub, G.H.; Liesen, J., Numerical solution of saddle point problems, Acta numer., 14, 1-137, (2005) · Zbl 1115.65034
[6] Cao, Z.-H., Positive stable block triangular preconditioners for symmetric saddle point problems, Appl. numer. math., 57, 899-910, (2007) · Zbl 1118.65021
[7] S.-L. Wu, C.-X. Li, Indefinite block triangular preconditioner for symmetric saddle point problems, Calcolo (to appear).
[8] Silvester, D.J.; Elman, H.C.; Ramage, A., IFISS: incompressible flow iterative solution software
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