2017/06/23 by Jeremy K. Mason, Mason, Jeremy K.
Engineering · #41A05 #41A20 #65D05 #Engineering Applied Research #FOS: Mathematics #Mechanical stress and fatigue analysis #Numerical Analysis (math.NA) #Vibration and Dynamic Analysis
paper · pdf · doi:10.48550/arxiv.1706.07776
openalex publication_date 2017/06/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The Floater--Hormann family of rational interpolants do not have spurious poles or unattainable points, are efficient to calculate, and have arbitrarily high approximation orders. One concern when using them is that the amplification of rounding errors increases with approximation order, and can make balancing the interpolation error and rounding error difficult. This article proposes to modify the Floater--Hormann interpolants by including additional local polynomial interpolants at the ends of the interval. This appears to improve the conditioning of the interpolants and allow higher approximation orders to be used in practice.