Computer Science – Numerical Analysis
Scientific paper
2010-03-24
Computer Science
Numerical Analysis
18 pages, submitted to the Journal of Scientific Computing.
Scientific paper
In this paper, we consider methods to compute the coefficients of interpolants relative to a basis of polynomials satisfying a three-term recurrence relation. Two new algorithms are presented: the first constructs the coefficients of the interpolation incrementally and can be used to update the coefficients whenever a nodes is added to or removed from the interpolation. The second algorithm, which constructs the interpolation coefficients by decomposing the Vandermonde-like matrix iteratively, can not be used to update or downdate an interpolation, yet is more numerically stable than the first algorithm and is more efficient when the coefficients of multiple interpolations are to be computed over the same set of nodes.
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