Linear extrapolation is the process of estimating a value of f(x) that lies outside the range of the known independent variables. Given the data points (x1, y1) and (x2, y2), where x is the chosen data point, the formula for linear extrapolation is: f(x) = y1 + ((x - x1) / (x2 - x1)) * (y2 - y1)
Extrapolation is used for data prediction in several different fields, provided there is sufficient historic data. Future weather patterns, sensor signals, population growth and geographical positions are all predicted using extrapolation.
Unlike linear interpolation, which estimates values within the range of the known data points, linear extrapolation is prone to error, and it has a higher risk of producing meaningless data. Therefore, to obtain the best-possible data, it is important to determine the nature of the function. Linear extrapolation provides acceptable data if the function is linear. However, if the function is not linear, choosing values close to the known data increases the odds of producing meaningful data.
Many students find Matlab useful to solve extrapolation problems, especially problems involving high-order polynomials, as they are significantly more complicated than problems involving linear functions. Matlab has several built-in functions that calculate extrapolated values from linear, polynomial and conic functions.