BOAS said:
mesa said:That is as far as I have gotten (can't afford the $38). I don't need the whole paper, although it would be nice to have just the algorithm would be good enough for now.
As I understand it they use AGM and elliptic integrals of the first kind in order to compute large decimal approximations for certain values of the gamma function with very few steps, but that is about all I know of it so far :P
BOAS said:I have access to it, and if it's not objectionable to you, I'm happy to email you a pdf.
Did you see this discussion?
http://math.stackexchange.com/quest...-gamma-function-to-high-precision-efficiently
I have literally no idea what they're talking about, but perhaps they discuss it in enough detail for you.
Borwein's/Zucker's fast algorithm is a method for computing the gamma function, which is a mathematical function used to find the area under a curve. It is named after mathematicians Jonathan Borwein and Ira Zucker, who developed the algorithm in 1991. It is known for its speed and accuracy compared to other methods.
The fast algorithm uses a combination of numerical integration and approximation techniques to compute the gamma function. It involves breaking the function into smaller, more manageable pieces and then using a series of approximations to find the final result. This approach reduces the number of calculations needed and improves the speed of computation.
One of the main advantages of this algorithm is its speed. It can compute the gamma function much faster than other methods, making it useful for applications that require quick calculations. Additionally, the algorithm is also known for its accuracy, producing results that are very close to the true value of the gamma function.
While Borwein's/Zucker's fast algorithm is generally very efficient, it does have some limitations. For example, it may not work well for very large or very small values of the gamma function, as the approximations used in the algorithm may not be accurate enough in these cases. Additionally, the algorithm may not be suitable for certain types of functions that are not well-behaved.
The fast algorithm for the gamma function has many practical applications in fields such as physics, engineering, and statistics. It is used to calculate various quantities, such as probabilities, areas under curves, and energy levels. It is also used in computer software and algorithms that require quick and accurate computations of the gamma function.