interpolation
(noun)
the process of estimating the value of a function at a point from its values at nearby points
Examples of interpolation in the following topics:
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The Discrete Fourier Transform
- Now we will compute the coefficients in such a way that $p$ interpolates (i.e., fits exactly) the data at each $x_k$ :
- $f_n$ are the data and $c_k$ are the harmonic coefficients of a trigonometric function that interpolates the data.
- Now, of course, there are many ways to interpolate data, but it is a theorem that the only way to interpolate with powers of $e^{i 2 \pi x}$ is Equation 4.6.3.
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Numerical Integration
- A large class of quadrature rules can be derived by constructing interpolating functions which are easy to integrate.
- Typically these interpolating functions are polynomials.
- The simplest method of this type is to let the interpolating function be a constant function (a polynomial of degree zero) which passes through the point $\left(\frac{(a+b)}{2}, f\left(\frac{(a+b)}{2}\right)\right)$.
- The interpolating function may be an affine function (a polynomial of degree 1) which passes through the points $(a, f(a))$ and $(b, f(b))$.
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The Regression Method
- Sometimes statisticians will use interpolation to predict data points within the range of known data points.
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Percentiles
- When R is not an integer, we compute the Pth percentile by interpolation as follows:
- Interpolate by multiplying the difference between the scores by FR and add the result to the lower score.
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The Linear Algebra of the DFT
- The summation in the Fourier interpolation is therefore a matrix-vector inner product.
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A Graph of Averages
- The line is a model that can be used to make predictions, whether it is interpolation or extrapolation.
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Solutions to Exercises in Chapter 13
- NOTE: The process of predicting inside of the observed x values in the data is called interpolation.
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Applications of Statistics
- It can include extrapolation and interpolation of time series or spatial data and can also include data mining.
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Fundamentals of Statistics
- It can include extrapolation and interpolation of time series or spatial data, and can also include data mining.
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Police
- The International Criminal Police Organization (ICPO), widely known as INTERPOL, is an organization facilitating international police cooperation.