An Easy Method to Accelerate an Iterative Algebraic Solver, part II
- Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
This study is a companion to [Yao, Journal of Computational Physics267(2014)]. We provide a compact alternative development of Yao’s method to accelerate to order 2n–1 a fixed-point iterative scheme with an original convergence-rate of ordern. Using this approach, we show how to further improve the order of convergence by increasings, the number of steps per iteration. This scheme extends to arbitrarily high order without extra derivative evaluations per iteration. We discuss the efficiency of the new methods, including s = 2 (Yao’s method), and compare to that of the original method as a function of n; and we consider the efficiency for systems of equations of system-size M. For n = 2 and large M, we find that the multi-step scheme peaks in efficiency at about s ln s ~ M function evaluations, where its computational speed is several times faster than Newton’s method.
- Research Organization:
- Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
- Sponsoring Organization:
- USDOE National Nuclear Security Administration (NNSA)
- DOE Contract Number:
- AC52-07NA27344
- OSTI ID:
- 1497320
- Report Number(s):
- LLNL-JRNL-652972; 773489
- Journal Information:
- Proposed Journal Article, unpublished, Vol. 2014; ISSN 9999-9999
- Publisher:
- See Research Organization
- Country of Publication:
- United States
- Language:
- English
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