Numerical Analysis Questions Medium
Interpolation is a technique used in numerical analysis to estimate the value of a function between two known data points. It involves constructing a function that passes through the given data points and can be used to approximate the value of the function at any intermediate point.
The process of interpolation typically involves the following steps:
1. Given a set of data points (x1, y1), (x2, y2), ..., (xn, yn), where xi represents the independent variable and yi represents the corresponding dependent variable.
2. Choose an interpolation method or technique that best suits the problem at hand. Some commonly used interpolation methods include linear interpolation, polynomial interpolation, spline interpolation, and trigonometric interpolation.
3. Based on the chosen method, construct an interpolating function that passes through the given data points. The form of the interpolating function depends on the interpolation method used. For example, in linear interpolation, the interpolating function is a straight line connecting two adjacent data points.
4. Evaluate the interpolating function at the desired intermediate point to estimate the value of the function at that point. This can be done by substituting the intermediate point's x-value into the interpolating function and calculating the corresponding y-value.
5. Repeat steps 3 and 4 as needed for multiple intermediate points.
It is important to note that interpolation assumes that the function being approximated is smooth and continuous between the given data points. The accuracy of the interpolation depends on the quality and density of the data points, as well as the chosen interpolation method.