what are the differences between spline and Lagrange interpolation, and are there any other kinds that might be similar that perform well ?
2026-03-29 13:20:28.1774790428
different Interpolation techniques
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Lagrange is a single polynomial, whereas spline interpolation is piecewise polynomial (often of cubic degree).
Polynomials are known to be unsuitable for a large number of points, they start oscillating unwieldy. On the other hand, they are infinitely differentiable, offering a maximum degree of continuity.
Reciprocally, (cubic) splines can deal with an arbitrary number of points but offer value, slope and curvature continuity only.
Hermite interpolation (Cardinal and Catmull-Rom splines) is a simple cubic method that can be computed locally, requiring only the knowledge of four points per interval. It provides value and slope continuity.
Lanczos interpolation, based on the sinc function, can be used on uniformly sampled data. It performs perfect signal reconstruction in case of a band-limited signal.
Other big names that you will find in the literature (Bézier, B-splines, NURBS) are approximation rather than interpolation methods.