Post Reply 
(HP15C)(HP67)(HP41C) Bernoulli Polynomials
08-29-2023, 09:16 PM
Post: #8
RE: (HP15C)(HP67)(HP41C) Bernoulli Polynomials
The problem here is that all useful methods of calculating Bernoulli numbers involve fairly large numbers, and the classic hp's can only represent numbers < 10^10 exactly. Albert's method using Stirling numbers may be better than nested summation but will still see cancellation errors for n > 16.

One of my favorite methods uses Euler zigzag numbers. The numbers involved are smaller than factorials, and computing the zigzag numbers requires only addition. Also, this method requires only one division at the end, which prevents rounding errors from accumulating. However, i have not compared the two methods directly and there may be little or no improvement in practice.
Find all posts by this user
Quote this message in a reply
Post Reply 


Messages In This Thread
RE: (HP15C)(HP67)(HP41C) Bernoulli Polynomials - John Keith - 08-29-2023 09:16 PM



User(s) browsing this thread: 1 Guest(s)