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Numerical Algebra, Control and Optimization (NACO)
 

On product-type generalized block AOR method for augmented linear systems

Pages: 797 - 809, Volume 2, Issue 4, December 2012      doi:10.3934/naco.2012.2.797

 
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Fang Chen - Department of Mathematical Sciences, Xi'an Jiaotong University, Xi'an 710049, China (email)
Ning Gao - Department of Mathematical Sciences, Xi'an Jiaotong University, Xi'an 710049, China (email)
Yao- Lin Jiang - Department of Mathematical Sciences, Xi'an Jiaotong University, Xi'an 710049, China (email)

Abstract: The generalized inexact accelerated overrelaxation ( GIAOR) method was presented by Bai, Parlett and Wang (Numer. Math. 102(2005)1-38) for solving the augmented system of linear equations. In this paper, a product-type generalized block AOR ( PGBAOR ) method is proposed, which is a two-step generalization of the GIAOR method. Both convergence and semi-convergence of the PGBAOR method are proved for the nonsingular and the singular augmented linear systems.

Keywords:  Augmented linear system, block AOR method, convergence, semi-convergence.
Mathematics Subject Classification:  Primary: 65F10, 65F50.

Received: December 2011;      Revised: August 2012;      Available Online: November 2012.

 References