interpolation

Examples of interpolation in the following topics:

• 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.

• 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 $(b, f(b))$.

• 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.