Publication

Generalized Interpolation: Higher Quality at no Additional Cost

Michaël Unser, Thierry Blu, Philippe Thévenaz
1999
Conference Papers

Abstract

We extend the classical interpolation method to generalized interpolation. This extension is done by replacing the interpolating function by a non-interpolating function that is applied to prefiltered data, in order to preserve the interpolation condition. We show, both theoretically and practically, that this approach performs much better than classical methods, for the same computational cost.

Official source

https://infoscience.epfl.ch/entities/publication/53a86ad7-9cbd-49f1-82e2-6bdd52d4051b

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Michaël Unser, Thierry Blu, Philippe Thévenaz
1999
Conference Papers

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/53a86ad7-9cbd-49f1-82e2-6bdd52d4051b

About this result

Related concepts (23)

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 range of a discrete set of known data points. In engineering and science, one often has a number of data points, obtained by sampling or experimentation, which represent the values of a function for a limited number of values of the independent variable. It is often required to interpolate; that is, estimate the value of that function for an intermediate value of the independent variable.

Polynomial interpolation

In numerical analysis, polynomial interpolation is the interpolation of a given bivariate data set by the polynomial of lowest possible degree that passes through the points of the dataset. Given a set of n + 1 data points , with no two the same, a polynomial function is said to interpolate the data if for each . There is always a unique such polynomial, commonly given by two explicit formulas, the Lagrange polynomials and Newton polynomials.

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 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-ten polynomial to all of them.

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Generalized Interpolation: Higher Quality at no Additional Cost

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