Abstract
The central part of this chapter is the theorem of Young about SOR convergence. It requires ‘consistently ordered matrices’. This is a more involved structural matrix property. In Section 4.1, we consider the simpler structure of 2-cyclic matrices. Sections 4.3–4.5 investigate the Richardson, Jacobi, and Gauss–Seidel iteration in this case. Section 4.6 contains the analysis of the SOR iteration. Finally, Section 4.7 presents numerical results for the model problem.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2016 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Hackbusch, W. (2016). Analysis of Classical Iterations Under Special Structural Conditions. In: Iterative Solution of Large Sparse Systems of Equations. Applied Mathematical Sciences, vol 95 . Springer, Cham. https://doi.org/10.1007/978-3-319-28483-5_4
Download citation
DOI: https://doi.org/10.1007/978-3-319-28483-5_4
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-28481-1
Online ISBN: 978-3-319-28483-5
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)