Interpolation

:This article is about interpolation in mathematics. See also interpolation (music) and interpolation (manuscripts).

Spline interpolation

Main article: spline interpolation

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Remember that linear interpolation uses a linear function for each of intervals . Spline interpolation uses low-degree polynomials in each of the intervals, and chooses the polynomial pieces such that they fit smoothly together. The resulting function is called a spline.

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For instance, the natural cubic spline is piecewise cubic and twice continuously differentiable. Furthermore, its second derivative is zero at the end points. The natural cubic spline interpolating the points in the table above is given by

Related Topics:
Natural cubic spline - Piecewise

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: f(x) = left{ egin{matrix}

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