, Volume 46, Issue 4, pp 261–266

A note on double splittings of different monotone matrices


DOI: 10.1007/s10092-009-0011-z

Cite this article as:
Miao, SX. & Zheng, B. Calcolo (2009) 46: 261. doi:10.1007/s10092-009-0011-z


Comparison theorems between the spectral radii of different matrices are a useful tool for judging the efficiency of preconditioners. For single splittings of different monotone matrices, Elsner et al. (Linear Algebra Appl. 363:65–80, 2003) gave out comparison theorems for spectral radii. For double splittings, some convergence and comparison theorems of a monotone matrix are presented by Shen et al. (Comput. Math. Appl. 51:1751–1760, 2006). In this note we give the comparison theorem for the spectral radii of matrices arising from double splittings of different monotone matrices.


Spectral radius Comparison theorem Double splitting Monotone matrix 

Mathematics Subject Classification (2000)

65F10 65F15 

Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsLanzhou UniversityLanzhouPeople’s Republic of China
  2. 2.College of Mathematics and Information ScienceNorthwest Normal UniversityLanzhouPeople’s Republic of China

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