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Mathematics of Computation

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Efficient algorithms for polynomial interpolation and numerical differentiation

Author: Fred T. Krogh
Journal: Math. Comp. 24 (1970), 185-190
MSC: Primary 65.20
MathSciNet review: 0258240
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Abstract: Algorithms based on Newton's interpolation formula are given for: simple polynomial interpolation, polynomial interpolation with derivatives supplied at some of the data points, interpolation with piecewise polynomials having a continuous first derivative, and numerical differentiation. These algorithms have all the advantages of the corresponding algorithms based on Aitken-Neville interpolation, and are more efficient.

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Keywords: Interpolation, numerical differentiation, Newton's interpolation formula, Aitken interpolation, Neville interpolation, Lagrange interpolation, Hermite interpolation, spline function
Article copyright: © Copyright 1970 American Mathematical Society

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