Everything about Linear interpolation

🧭 Start here: a 6-step reading path

1. Read the overview: Linear interpolationA 5-minute orientation
2. Skim a recent paper: Hydromagnetic flow and thermal interpretations of Cross hybrid nanofluid influenced by linear, nonlinear and quadratic thermal radiations for any Prandtl numberInfluential work since 2022
3. Pick up a classic book: Interpolation functors and interpolation spacesThe most-reprinted book on the subject
4. Read the landmark paper: Interpolation of linear operatorsCited 416 times
5. Go sideways: Spline interpolationA closely related topic
6. Go sideways: Polynomial interpolationA closely related topic

🏆 Landmark papers (most cited)

• Interpolation of linear operators

  Elias M. Stein · 1956 · Transactions of the American Mathematical Society · 416 citations

• Linear Interpolation Revitalized

  T. Blu, P. Thevenaz, M. Unser · 2004 · IEEE Transactions on Image Processing · 386 citations

• Linear Methods for Image Interpolation

  Pascal Getreuer · 2011 · Image Processing On Line · 110 citations

• Piecewise-Linear Interpolation between Polygonal Slices

  Gill Barequet, Micha Sharir · 1996 · Computer Vision and Image Understanding · 94 citations

• Linear interpolation of histograms

  A.L Read · 1999 · Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment · 93 citations

• Reflexivity, Algebraic Reflexivity and Linear Interpolation

  David R. Larson · 1988 · American Journal of Mathematics · 74 citations

• Some results in linear interpolation theory

  S. Kay · 1983 · IEEE Transactions on Acoustics, Speech, and Signal Processing · 48 citations

• Compact linear mappings between interpolation spaces

  Arne Persson · 1964 · Arkiv för Matematik · 46 citations

🆕 Influential since 2022

• Hydromagnetic flow and thermal interpretations of Cross hybrid nanofluid influenced by linear, nonlinear and quadratic thermal radiations for any Prandtl number

  S. Shaw, S.S. Samantaray, A. Misra · 2022 · International Communications in Heat and Mass Transfer · 164 citations

• All linear fractional derivatives with power functions’ convolution kernel and interpolation properties

  Babak Shiri, Dumitru Baleanu · 2023 · Chaos, Solitons & Fractals · 37 citations

• Bayesian interpolation with deep linear networks

  Boris Hanin, Alexander Zlokapa · 2023 · Proceedings of the National Academy of Sciences · 23 citations

• PM2.5 Time Series Imputation with Moving Averages, Smoothing, and Linear Interpolation

  Anibal Flores, Hugo Tito-Chura, Osmar Cuentas-Toledo · 2024 · Computers · 21 citations

• JNMR: Joint Non-Linear Motion Regression for Video Frame Interpolation

  Meiqin Liu, Chenming Xu, Chao Yao · 2023 · IEEE Transactions on Image Processing · 15 citations

📚 Books worth reading

• Interpolation functors and interpolation spacesBrudnyĭ, I͡U. A., Yu A. Brudnyi · 1991
• 📕Extension and interpolation of linear operators and matrix functionsI. Gohberg · 1990
• Interpolation Schur Functions And Moment Problems IiBernd Kirstein · 2012
• 📕Interpolation of Linear OperatorsS. G. Krein, Ju. I. Petunin · 2002
• 📕Interpolation dans les especesNimet Deutsch · 1968
• Interpolation And Regression Models For The Chemical Engineer Solving Numerical ProblemsFlavio Manenti · 2010
• 📕Time-variant systems and interpolationGohberg, I. · 1992
• 📕Entropy and multivariable interpolationGelu Popescu · 2006

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

🔗 Related topics

• 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…
• 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…
• Interpolation In the mathematical field of numerical analysis, interpolation is a type of estimation, a method of constructing (finding) new data points based on the…
• Vandermonde matrix In linear algebra, a Vandermonde matrix, named after Alexandre-Théophile Vandermonde, is a matrix with the terms of a geometric progression in each row:…
• Interpolation space In the field of mathematical analysis, an interpolation space is a space which lies "in between" two other Banach spaces. The main applications are in…
• Lagrange polynomial In numerical analysis, the Lagrange interpolating polynomial is the unique polynomial of lowest degree that interpolates a given set of data. Given a data…
• Simpson's rule In numerical integration, Simpson's rules are several approximations for definite integrals, named after Thomas Simpson (1710–1761). The most basic of…
• Linear function (calculus) In calculus and related areas of mathematics, a linear function from the real numbers to the real numbers is a function whose graph (in Cartesian coordinates)…