What is piecewise interpolation

1. What is piecewise constant interpolation?
2. What is piecewise polynomial?
3. What is the most common form of piecewise polynomial interpolation?
4. What are the two methods of interpolation?

What is piecewise constant interpolation?

Piecewise constant interpolation

The simplest interpolation method is to locate the nearest data value, and assign the same value.

What is piecewise polynomial?

6.1 PIECEWISE POLYNOMIALS

A piecewise polynomial of order k with break sequence ξ (necessarily strictly increasing) is, by definition, any function f that, on each of the half-open intervals [ξ_j ‥ ξ_j+1), agrees with some polynomial of degree < k. The term 'order' used here is not standard but handy.

What is the most common form of piecewise polynomial interpolation?

3.2 Linear Interpolation

Piecewise linear interpolation [21] is by far the most popular interpolation technique that finds numeral application in signal and image processing due to its faster performance.

What are the two methods of interpolation?

They are: Linear Interpolation Method – This method applies a distinct linear polynomial between each pair of data points for curves, or within the sets of three points for surfaces. Nearest Neighbour Method – This method inserts the value of an interpolated point to the value of the most adjacent data point.