Piecewise polynomial interpolation example

1. What is piecewise polynomial interpolation?
2. What is a piecewise polynomial?
3. What is piecewise constant interpolation?

What is piecewise polynomial interpolation?

A piecewise polynomial function is defined as. Pj(x)=∑kr=1ajr(x−xj)r(12) Hence, the piecewise polynomial interpolation problem is to determine the coefficients ajr for all of the intervals such that the resulting interpolant has desirable properties.

What is a 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 piecewise constant interpolation?

Piecewise constant interpolation

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