Definition:Romberg Integration

Definition

Let $\closedint a b$ be a closed real interval.

Let $f$ be a function over $\closedint a b$.

Let Richardson extrapolation be iteratively applied with repeated trapezium rule approximations having subinterval lengths:

$h_k = \dfrac {b - a} {2^{k - 1} }$

for $k = 1, 2, \ldots$

This process is known as Romberg integration.

Also see

• Results about Romberg integration can be found here.

Source of Name

This entry was named for Werner Romberg.

Historical Note

Romberg integration was invented by Werner Romberg in $1955$.

Sources

• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): Romberg integration