Spline Interpolation Algorithm

See: Runge's Phenomenon, Mathematics, Numerical Analysis, Interpolation, Piecewise, Polynomial, Spline (Mathematics), Polynomial Interpolation, Interpolation Error.

References

(Wikipedia, 2021) ⇒ https://en.wikipedia.org/wiki/Spline_interpolation Retrieved:2021-9-5.
- In the mathematical field of numerical analysis, spline interpolation is a form of interpolation where the interpolant is a special type of piecewise polynomial called a spline. That is, instead of fitting a single, high-degree polynomial to all of the values at once, spline interpolation fits low-degree polynomials to small subsets of the values, for example, fitting nine cubic polynomials between each of the pairs of ten points, instead of fitting a single degree-ten polynomial to all of them. Spline interpolation is often preferred over polynomial interpolation because the interpolation error can be made small even when using low-degree polynomials for the spline. Spline interpolation also avoids the problem of Runge's phenomenon, in which oscillation can occur between points when interpolating using high-degree polynomials.