Spline interpolation

<p>In the <a href="/facts/Mathematics/pxTouaz4">mathematical</a> field of <a href="/facts/Numerical_analysis/QT9cYa9z">numerical analysis</a>, spline interpolation is a form of <a href="/facts/Interpolation/8PyetX4f">interpolation</a> where the interpolant is a special type of <a href="/facts/Piecewise/nlQwptpe">piecewise</a> <a href="/facts/Polynomial/Lzak8VVx">polynomial</a> called a <a href="/facts/Spline_(mathematics)/yafkQtqp">spline</a>. 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-nine polynomial to all of them. Spline interpolation is often preferred over <a href="/facts/Polynomial_interpolation/DmnuxaKT">polynomial interpolation</a> because the <a href="/facts/Interpolation_error/8PyetX4f">interpolation error</a> can be made small even when using low-degree polynomials for the spline. Spline interpolation also avoids the problem of <a href="/facts/Runge%2527s_phenomenon/641beUAR">Runge's phenomenon</a>, in which oscillation can occur between points when interpolating using high-degree polynomials.
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Spline interpolation open-in-new

Spline interpolation