1. Introduction to Numerical Analysis I
MATH/CMPSC 455
Introduction to Numerical Analysis I
Romberg Integration

2. Romberg Integration Recursive formula of the composite trapezoid rule
Extrapolation (low order formula – high order formula)

3. Recursive formula of the composite trapezoid rule
Let denote the composite trapezoid rule with 2n subintervals, we have

4. Extrapolation Error of the composite trapezoid rule
Idea: We can extrapolate with the second-order formula, cancel the second order term, and yield a fourth-order formula; extrapolation with the resulting fourth-order formula gives a sixth-order formula, and so on.

5. 4-th order formula
6-th order formula

6. Romberg Table