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In this paper, we consider methods to compute the coefficients ofinterpolants relative to a basis of polynomials satisfying a three-termrecurrence relation. Two new algorithms are presented: the first constructs thecoefficients of the interpolation incrementally and can be used to update thecoefficients whenever a nodes is added to or removed from the interpolation.The second algorithm, which constructs the interpolation coefficients bydecomposing the Vandermonde-like matrix iteratively, can not be used to updateor downdate an interpolation, yet is more numerically stable than the firstalgorithm and is more efficient when the coefficients of multipleinterpolations are to be computed over the same set of nodes.

Efficient Construction, Update and Downdate Of The Coefficients Of Interpolants Based On Polynomials Satisfying A Three-Term Recurrence Relation