Extended Continuous Interpolation

by Willard M. Snyder,

Serial Information: Journal of the Hydraulics Division, 1967, Vol. 93, Issue 5, Pg. 261-282

Document Type: Journal Paper


A method of interpolation is developed which generates a locus of values having mathematical continuity and having continuous first and second derivatives. The locus is generated by passing a six-point interpolating system through any extended range of data. The value of this method of interpolation is found in the first derivative. Since the second derivative is finitely continuous, the first derivative is smoothly continuous. Therefore, this system can be used effectively to interpolate for slopes of functions defined only at discrete intervals. It provides for point slopes rather than interval slopes of usual finite difference methods. The interpolation locus within any six-point set is a polynomial expression of those points. However, the complete locus through extended ranges of data is essentially form-free.

Subject Headings: Slopes | Finite difference method | Polynomials

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