Definition:Arithmetic-Geometric Mean/Iteration

Definition
Let $a$ and $b$ be numbers.

Let $\sequence {a_n}$ and $\sequence {b_n}$ be defined as the recursive sequences:

where:

The above process is known as the arithmetic-geometric mean iteration.

Also see

 * Arithmetic-Geometric Mean Iteration Converges Quadratically to Common Limit


 * Definition:Arithmetic-Geometric Mean