Modified block preconditioner for generalized saddle point matrices with highly singular(1,1) blocks

ABSTRACT

In this paper, based on the preconditioners presented by Zhang [A new preconditioner for generalized saddle matrices with highly singular(1,1) blocks. Int J Comput Maths. 2014;91(9):2091-2101], we consider a modified block preconditioner for generalized saddle point matrices whose coefficient matrices have singular (1,1) blocks. Moreover, theoretical analysis gives the eigenvalue distribution, forms of the eigenvectors and the minimal polynomial. Finally, numerical examples show the eigenvalue distribution with the presented preconditioner and confirm our analysis.

KEYWORDS:

• Saddle point matrices
• Krylov subspace methods
• generalized saddle point matrices
• minimal polynomial
• preconditioners

MATHEMATICS SUBJECT CLASSIFCATIONS:

• 65F10
• 65F15

Disclosure statement

No potential conflict of interest was reported by the author.

Additional information

Funding

This research is supported by the National Natural Science Foundation of China [11226337, 11501525], Excellent Youth Foundation of Science Technology Innovation of Henan Province [184100510004], Science Technology Innovation Talents in Universities of Henan Province [16HASTIT040, 17HASTIT012], Aeronautical Science Foundation of China [2016ZG55019, 2017ZD55014], Project of Youth Backbone Teachers of Colleges and Universities of Henan Province [2015GGJS-003, 2015GGJS-179], Advanced Technological Research Project of Henan Province [182102110129], Henan Province Postdoctoral Science Foundation [2013031], Research on Innovation Ability Evaluation Index System and Evaluation Model [142400411268].