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The Floater--Hormann family of rational interpolants do not have spuriouspoles or unattainable points, are efficient to calculate, and have arbitrarilyhigh approximation orders. One concern when using them is that theamplification of rounding errors increases with approximation order, and canmake balancing the interpolation error and rounding error difficult. Thisarticle proposes to modify the Floater--Hormann interpolants by includingadditional local polynomial interpolants at the ends of the interval. Thisappears to improve the conditioning of the interpolants and allow higherapproximation orders to be used in practice.

Improved conditioning of the Floater--Hormann interpolants