Full linear multistep methods as root-finders

Bart S. van Lith, Jan H.M. ten Thije Boonkkamp and Wilbert L. IJzerman

Applied Mathematics and Computation, 2018, vol. 320, issue C, 190-201

Abstract: Root-finders based on full linear multistep methods (LMMs) use previous function values, derivatives and root estimates to iteratively find a root of a nonlinear function. As ODE solvers, full LMMs are typically not zero-stable. However, used as root-finders, the interpolation points are convergent so that such stability issues are circumvented. A general analysis is provided based on inverse polynomial interpolation, which is used to prove a fundamental barrier on the convergence rate of any LMM-based method. We show, using numerical examples, that full LMM-based methods perform excellently. Finally, we also provide a robust implementation based on Brent’s method that is guaranteed to converge.

Keywords: Root-finder; Nonlinear equation; Linear multistep methods; Iterative methods; Convergence rate (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:320:y:2018:i:c:p:190-201

DOI: 10.1016/j.amc.2017.09.003

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