Numerical Analysis Questions Medium
Interpolation and extrapolation are both techniques used in numerical analysis to estimate values between or beyond a given set of data points. However, they differ in terms of the range of estimation.
Interpolation involves estimating values within the range of the given data points. It is used to find values between known data points by constructing a function or curve that passes through these points. Interpolation assumes that the relationship between the data points is continuous and can be accurately represented by the constructed function. This technique is commonly used to fill in missing data or to estimate values at specific points within a given range.
On the other hand, extrapolation involves estimating values beyond the range of the given data points. It is used to predict values outside the known data range by extending the constructed function or curve beyond the given data points. Extrapolation assumes that the relationship between the data points continues beyond the known range and can be accurately represented by the extended function. However, extrapolation is generally considered less reliable than interpolation because it relies on assumptions about the behavior of the data outside the known range, which may not always hold true.
In summary, interpolation is used to estimate values within the range of the given data points, while extrapolation is used to estimate values beyond the range of the given data points. Interpolation is generally considered more reliable than extrapolation due to the assumptions involved in extending the data beyond the known range.