2017/02/10 by Bart S. van Lith, van Lith, Bart S., J. H. M. ten Thije Boonkkamp +3
Computer Science · Engineering · #FOS: Mathematics #Matrix Theory and Algorithms #Numerical Analysis (math.NA) #Numerical Methods and Algorithms #Power System Optimization and Stability
paper · pdf · doi:10.48550/arxiv.1702.03174
openalex publication_date 2017/02/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.