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Everything about Interpolation
Method for estimating new data within known data points
In the mathematical field of numerical analysis, interpolation is a type of estimation, a method of constructing (finding) new data points based on the range of a discrete set of known data points. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: InterpolationA 5-minute orientation
- Skim a recent paper: NHITS: Neural Hierarchical Interpolation for Time Series ForecastingInfluential work since 2022
- Pick up a classic book: A short course in interpolationThe most-reprinted book on the subject
- Read the landmark paper: Bayesian InterpolationCited 3,630 times
- Go sideways: Linear interpolationA closely related topic
- Go sideways: Spline interpolationA closely related topic
📖 Definitions
Noun An abrupt change in elements, with continuation of the first idea.
Noun The process of estimating the value of a function at a point from its values at nearby points.
Noun The process of interpolating: including and processing externally-fetched data in a document or program.
Noun That which is introduced or inserted; in contexts of content analysis of centuries-old texts, especially something foreign or spurious.
🏆 Landmark papers (most cited)
Bayesian Interpolation
A stable and accurate convective modelling procedure based on quadratic upstream interpolation
Cubic convolution interpolation for digital image processing
Chemical mass transfer in magmatic processes IV. A revised and internally consistent thermodynamic model for the interpolation and extrapolation of liquid-solid equilibria in magmatic systems at elevated temperatures and pressures
Material interpolation schemes in topology optimization
Monotone Piecewise Cubic Interpolation
Improved Global Sea Surface Temperature Analyses Using Optimum Interpolation
A New Method of Interpolation and Smooth Curve Fitting Based on Local Procedures
🆕 Influential since 2022
NHITS: Neural Hierarchical Interpolation for Time Series Forecasting
Interpolation consistency training for semi-supervised learning
Neural network guided interpolation for mapping canopy height of China's forests by integrating GEDI and ICESat-2 data
Surprises in high-dimensional ridgeless least squares interpolation
Quadratic Interpolation Optimization (QIO): A new optimization algorithm based on generalized quadratic interpolation and its applications to real-world engineering problems
📚 Books worth reading
A short course in interpolationE. T. Whittaker, George Robinson · 1923
A course in interpolation and numerical integration for the mathematical laboratoryDavid Gibb · 1915
Birkhoff interpolationG. G. Lorentz · 1983- 📕Interpolation and approximation by rational functions in the complex domainJ. L. Walsh · 1935
Introduction to numerical analysisFrancis Begnaud Hildebrand · 1956- 📕Interpolation and allied tablesGreat Britain Nautical Almanac Office · 1949
- 📕Calculus of finite differencesKároly Jordán · 1939
InterpolationJ. F. Steffensen · 1927
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
- Linear interpolation In mathematics, linear interpolation is a method of function approximation using linear polynomials to construct new data points within the range of a…
- Spline interpolation In the mathematical field of numerical analysis, spline interpolation is a form of interpolation where the interpolant is a special type of piecewise polynomial…
- Basis function In mathematics, a basis function is an element of a particular basis for a function space. Every function in the function space can be represented as a…
- Multivariate interpolation In numerical analysis, multivariate interpolation or multidimensional interpolation is interpolation on multivariate functions, having more than one variable…
- Polynomial interpolation In numerical analysis, polynomial interpolation is the interpolation of a given data set by the polynomial of lowest possible degree that passes through…
- List of numerical analysis topics This is a list of numerical analysis topics. Validated numerics Iterative method Rate of convergence — the speed at which a convergent sequence approaches…
- Runge's phenomenon In the mathematical field of numerical analysis, Runge's phenomenon (German: [ˈʁʊŋə]) is a problem of oscillation at the edges of an interval that occurs…
- Spline (mathematics) In mathematics, a spline is a function defined piecewise by polynomials. In interpolating problems, spline interpolation is often preferred to polynomial…