Understand the concept of interpolation and its applications in mathematics, computer graphics, and data science. This guide covers different interpolation techniques, including linear, polynomial, and spline interpolation, with practical examples for accurate estimation between data points.

1. Interpolation

2. Interpolation
In the mathematical field of numerical analysis, interpolation is a type of estimation, a method
of constructing (finding) new data points based on the range of a discrete set of known data
points.

3. Topics
Newton's Forward Interpolation
Newton Backward Interpolation
Lagrange Interpolation
Newton Divided Difference Interpolation

4. Newton's Forward Interpolation
The differences y1 – y0, y2 – y1, y3 – y2, ……, yn – yn–1 when denoted by dy0, dy1, dy2, ……,
dyn–1 are respectively, called the first forward differences. Thus, the first forward differences are
:

5. Newton Backward Interpolation
The differences y1 – y0, y2 – y1, ……, yn – yn–1 when denoted by dy1, dy2, ……, dyn, respectively,
are called first backward difference. Thus, the first backward differences are :

6. Lagrange Interpolation
The Lagrange interpolation formula is a way to find a polynomial which takes on certain values
at arbitrary points.

7. Newton Divided Difference Interpolation
Newton’s divided difference interpolation formula is a interpolation technique used when the
interval difference is not same for all sequence of values.

8. Thankyou