Piecewise quadratic interpolation

1. What is piecewise quadratic interpolation?
2. What is the difference between linear and quadratic spline interpolation?
3. What are the two methods of interpolation?
4. What is piecewise cubic Hermite interpolating polynomial?

What is piecewise quadratic interpolation?

Such a function g is called a piecewise linear interpolation if each of the polynomials on the subintervals are of degree less than or equal to 1. We say g is a piecewise quadratic interpolation if each of the polynomials on the subintervals are of degree less than or equal to 2.

What is the difference between linear and quadratic spline interpolation?

A- Linear Interpolation, the simplest form of interpolations to connect data points with straight line. B- Quadratic Interpolation, a strategy for improving the estimate is to introduce some curvature into the line connecting the points.

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.

What is piecewise cubic Hermite interpolating polynomial?

pchip interpolates using a piecewise cubic polynomial P ( x ) with these properties: On each subinterval x k ≤ x ≤ x k + 1 , the polynomial P ( x ) is a cubic Hermite interpolating polynomial for the given data points with specified derivatives (slopes) at the interpolation points.