What is interpolation?

Interpolation involves discovering a pattern in a set of data points to estimate the value between two points. Linear interpolation is one of the simplest methods of interpolation - a line connecting two points is used to estimate temporary values. Higher -order polynomials can replace linear functions for more accurate but more complex results. Interpolation can be contrasted with extrapolation, which is used to estimate the values ​​of outside sets of points instead of between them.

The discrete set of data points has points with two or more coordinates. In the typical XY scattering chart, the horizontal variable X is x and the vertical variable is Y. Data points with X and Y Coordinates can be brought into this chart for easy visualization. In practical applications, x and y represent the final number of real world. X generally represents an independent variable such as time or space, while y represents a dependent variable such as a population.

Often, the data can only be collected at discrete points. In an example of SLEarth's population can be edited only at certain times. These measurements could be brought as discrete data points on the XY chart.

If the census is only accepted every five years, it is not possible to know the exact population between the census. During linear interpolation, two data points are associated with a linear function. This means that a dependent variable (population) is assumed to change at constant speed and achieve another data point. If the population is a year after the need for a census, it could interpolate two data points linearly to estimate the mean value based on the connection line. It is usually obvious that the actual variable does not change between data points linearly, but this simplification is often accurate enough.

Sometimes, however, the linear interpolls represent too many mistakes. For example, the population shows exponential growth in many scenarios. In the exponThe growth rate itself is increasing - the higher population leads to more birth, which increases the overall level that the population increases. In the XY scattering land, this kind of behavior would show a trend that "curved up". A more accurate interpolation method may be suitable for this kind of study.

polynomial interpolation involves connecting numerous data points with polynomial function. In fact, the linear function is a simple variety of polynomial function - namely polynomial of the order. However, polynomials may have higher orders than one: Order two is a dish, order three is a cubic function, etc. The population data points can be better interpolated with a polynomic function than a linear function, as the first can curl up and down to match the data.