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Everything about Spline interpolation

Mathematical method

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-nine 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. Wikipedia →

🧭 Start here: a 6-step reading path

  1. Read the overview: Spline interpolationA 5-minute orientation
  2. Skim a recent paper: Modeling non-linear relationships in epidemiological data: The application and interpretation of spline modelsInfluential work since 2022
  3. Pick up a classic book: Birkhoff interpolationThe most-reprinted book on the subject
  4. Read the landmark paper: Cubic splines for image interpolation and digital filteringCited 914 times
  5. Go sideways: Polynomial interpolationA closely related topic
  6. Go sideways: Divided differencesA closely related topic

📖 Definitions

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🗂️ The subject at a glance

  1. Introduction
  2. Algorithm to find the interpolating cubic spline
  3. Example

🏆 Landmark papers (most cited)

🆕 Influential since 2022

📚 Books worth reading

Ranked by number of editions on Open Library, a rough measure of how lasting a book is.

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