The Convergence Rate of Block Preconditioned Systems Arising from LMF-based ODE Codes

Content Provider	Semantic Scholar
Author	Bertaccini, Daniele Ng, Michael K.
Copyright Year	2001
Abstract	AbstractThe solution of ordinary an partial differential equations using implicit linear multi-step formulas (LMF)is considered. More precisely, boundary value methods (BVMs), a class of methods based on implicit formulas will be taken into account in this paper. These methods require the solution of large and sparse linear systems $$\hat M$$ x = b. Block-circulant preconditioners have been propose to solve these linear systems. By investigating the spectral condition number of $$\hat M$$ , we show that the conjugate gradient method, when applied to solving the normalize preconditioned system, converges in at most O(log s) steps, where the integration step size is O(1/s). Numerical results are given to illustrate the effectiveness of the analysis.
Starting Page	433
Ending Page	450
Page Count	18
File Format	PDF HTM / HTML
DOI	10.1023/A:1021906926616
Volume Number	41
Alternate Webpage(s)	http://www.mat.uniroma2.it/bertaccini/papers/rateoc-BIT.pdf
Alternate Webpage(s)	https://doi.org/10.1023/A%3A1021906926616
Language	English
Access Restriction	Open
Content Type	Text
Resource Type	Article