interpolation

(noun)

the process of estimating the value of a function at a point from its values at nearby points

Related Terms

  • extrapolation
  • graph of averages

Examples of interpolation in the following topics:

  • The Discrete Fourier Transform

    • Now we will compute the coefficients in such a way that ppp interpolates (i.e., fits exactly) the data at each xkx_kx​k​​ :
    • fnf_nf​n​​ are the data and ckc_kc​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 ei2πxe^{i 2 \pi x}e​i2πx​​ is Equation 4.6.3.
  • 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 ((a+b)2,f((a+b)2))\left(\frac{(a+b)}{2}, f\left(\frac{(a+b)}{2}\right)\right)(​2​​(a+b)​​,f(​2​​(a+b)​​)).
    • The interpolating function may be an affine function (a polynomial of degree 1) which passes through the points (a,f(a))(a, f(a))(a,f(a)) and (b,f(b))(b, f(b))(b,f(b)).
  • The Regression Method

    • Sometimes statisticians will use interpolation to predict data points within the range of known data points.
  • 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.
  • The Linear Algebra of the DFT

    • The summation in the Fourier interpolation is therefore a matrix-vector inner product.
  • A Graph of Averages

    • The line is a model that can be used to make predictions, whether it is interpolation or extrapolation.
  • Solutions to Exercises in Chapter 13

    • NOTE: The process of predicting inside of the observed x values in the data is called interpolation.
  • Applications of Statistics

    • It can include extrapolation and interpolation of time series or spatial data and can also include data mining.
  • Fundamentals of Statistics

    • It can include extrapolation and interpolation of time series or spatial data, and can also include data mining.
  • Police

    • The International Criminal Police Organization (ICPO), widely known as INTERPOL, is an organization facilitating international police cooperation.
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