Convergence of block triangular preconditioner for generalized saddle point matrices with highly singular (1, 1) blocks. (2nd January 2016)

• Record Type: Journal Article
• Authors: Zhang, Li-Tao
• Is Part Of: International journal of modelling & simulation. Volume 36:Number 1/2(2016)
• Page Start: 2
• Page End: 7
• Publication Date: 2016-01-02
• Subjects: Saddle point matrices -- Krylov subspace methods -- Generalized saddle point matrices -- Minimal polynomial -- Preconditioners; 65F10 -- 65F15; Mathematical models -- Periodicals; Simulation methods -- Periodicals; Mathematical models; Simulation methods; Periodicals; 003.3
• DOI: 10.1080/02286203.2016.1142278
• Languages: English
• ISSNs: 0228-6203

Abstract

Abstract : In this paper, based on the preconditioners presented by Cao [J. Comput. Appl. Math. 2013;238:109–115], we present a block triangular 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 its minimal polynomial. Finally, numerical examples confirm our analysis when optimal parameters are chosen.