Adaptive Simpson and Romberg integration methods

[robve]

(03-26-2021 09:51 AM)Wes Loewer Wrote:  I love teaching Simpson's Rule to students, but...

Quote:Where would any book on numerical analysis be without Mr. Simpson and his “rule”? The classical formulas for integrating a function whose value is known at equally spaced steps have a certain elegance about them, and they are redolent with historical association. Through them, the modern numerical analyst communes with the spirits of his or her predecessors back across the centuries, as far as the time of Newton, if not farther. Alas, times do change; with the exception of two of the most modest formulas, the classical formulas are almost entirely useless. They are museum pieces, but beautiful ones.

~Numerical Recipes in C

Thanks for sharing the beautiful prose in Ch.4.1 on classical formulas.

One important reason to consider Romberg and Adaptive Simpson these days, as well as all of the classical formulas, is the inherent elegance and beauty of these methods.

Likewise, to appreciate vintage pocket machines (HP, SHARP, etc) with their limited hardware is a motivation to try to let them perform more powerful tasks than what they were designed for

So the focus is on (elegant when possible) pedagogical code examples in BASIC with C versions for reference.

I made some adjustments to the initial post to address reasonable questions and concerns when something was not clear. I misunderstood the HP-71B implementation, so that part is removed. The post is not specifically about the HP-71B and other posts already discuss that topic.

- Rob