An easier way to imagine this is by considering a case where you know the value of output at different input values. Now you wish to find out the value at a point which lies between that data set but whose value is unknown.
You will use interpolation to get a polynomial of order n if the number of known points is n+1. Now, put any input value between the data set and you’ll get the output.
The numerical analysis provides you with multiple methods for interpolation, some of them being LaGrange’s interpolation, Newton divided difference, newton’s forwards and backward difference and Neville interpolation. Where each of these methods has its special usage areas.
One popular application of interpolation is in the heat transfer equation. Consider a metal bar of uniform length which is being heated from one side and the other side is connected to a cold reservoir.
The value of temperature is known at equal intervals from the hot end to the cold end. Now, you’ve to tell the value of temperature at any specific point on the metal bar. Using interpolation you’ll generate a polynomial that can be used to get the value of temperature at that specific point.
There always exists a polynomial which passes through the desired set of point and there is one and only one such polynomial. The aim is to get a polynomial which is all close as possible to the original curve but as the number of points continues to increase the order of the polynomial increases and thus the calculation time also increases.
Try using interpolation in the next engineering project that you do. Compare your interpolated result with the results from the actual equation and find the relative error.
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