Interpolation

Definition:

Interpolation is the process of estimating the value of a function between two known values. This is often done by constructing a function that agrees with the known values at the data points, and then using this function to estimate the value at the desired point.

Types of Interpolation:

1. Linear Interpolation: In linear interpolation, a straight line is drawn between two known data points, and the value at the desired point is estimated based on the position of the point along the line.
2. Polynomial Interpolation: Polynomial interpolation involves fitting a polynomial function to the known data points, and then using this polynomial to estimate the value at the desired point.
3. Spline Interpolation: Spline interpolation uses piecewise polynomial functions to interpolate between data points, resulting in a smoother curve compared to polynomial interpolation.

Applications:

Interpolation is widely used in various fields such as engineering, computer graphics, geographic information systems (GIS), and finance. It is used to estimate values between known data points, and is particularly useful when working with continuous functions or datasets.

Study Guide:

To understand interpolation, it's important to grasp the following concepts:

1. Understanding of basic algebra and functions.
2. Familiarity with the concept of data points and plotting them on a graph.
3. Knowledge of how to find equations of lines and polynomials.
4. Understanding the idea of continuity and smoothness in curves.
5. Practice in using interpolation techniques to estimate values between data points.