# Interpolation And Extrapolation Examples Pdf

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## Interpolation and Extrapolation

Extrapolation is the process of taking data values at points x 1 , This is most commonly experienced when an incoming signal is sampled periodically and that data is used to approximate the next data point. For example, weather predictions take historic data and extrapolate a future weather pattern. Sensors may take the current and past voltages of an incoming signal and approximate a future value, perhaps attempting to compensate more appropriately. We have seen how to use interpolation to approximate values between points x 1 , However, if we are trying to approximate a value at a value outside the range of x values, the error increases significantly when using interpolation.

Interpolation is the process of using points with known values or sample points to estimate values at other unknown points. It can be used to predict unknown values for any geographic point data, such as elevation, rainfall, chemical concentrations, noise levels, and so on. The available interpolation methods are listed below. The Inverse Distance Weighting interpolator assumes that each input point has a local influence that diminishes with distance. It weights the points closer to the processing cell greater than those further away.

Extrapolation and interpolation are both used to estimate hypothetical values for a variable based on other observations. There are a variety of interpolation and extrapolation methods based on the overall trend that is observed in the data. These two methods have names that are very similar. We will examine the differences between them. For both methods, we assume a few things. We have identified an independent variable and a dependent variable. Through sampling or a collection of data, we have a number of pairings of these variables.

## Extrapolation

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In mathematics , extrapolation is a type of estimation , beyond the original observation range, of the value of a variable on the basis of its relationship with another variable. It is similar to interpolation , which produces estimates between known observations, but extrapolation is subject to greater uncertainty and a higher risk of producing meaningless results. Extrapolation may also mean extension of a method , assuming similar methods will be applicable. Extrapolation may also apply to human experience to project, extend, or expand known experience into an area not known or previously experienced so as to arrive at a usually conjectural knowledge of the unknown [1] e.

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