Arithmetic-Geometric Mean (AGM)
Calculates the arithmetic-geometric mean (AGM).
| \( Arithmetic-geometric\ mean\ AGM(a,b)\\ a_0=a,\ b_0=b\\ a_{n+1}={\large\frac{1}{2}}(a_n+b_n),\hspace{20px}b_{n+1}=\sqrt{a_nb_n},\\ AGM(a,b)=\displaystyle \lim_{n\to\infty}a_n=\displaystyle \lim_{n\to\infty}b_n\\ \) |
The calculation ends when the current value equals the previous value. Increasing the number of digits used in the calculation improves the accuracy of the AGM.
As the number of loop iterations increases, the number of significant digits doubles with each iteration: 5 digits, 10 digits, and 20 digits.
As the number of loop iterations increases, the number of significant digits doubles with each iteration: 5 digits, 10 digits, and 20 digits.
| \(\normalsize Arithmetic-geometric\ mean\ AGM(a,b)\\ (1)\ a_0=a,\ b_0=b\\ (2)\ a_{n+1}={\large\frac{1}{2}}(a_n+b_n),\hspace{20px}b_{n+1}=\sqrt{a_nb_n},\\ (3)\ a_1\ge a_2\ge a_3\ge ... \ge b_3\ge b_2\ge b_1\\ (4)\ AGM(a,b)=\displaystyle \lim_{n\to\infty}a_n=\displaystyle \lim_{n\to\infty}b_n\\ \) |
No customer feedback for this calculation yet.