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About 30 years ago I submitted an HP-41C program, about numerical integration, to the User's Library in Corvallis. This program used a new algorithm based on Lagrangian interpolation and allows the (x,y) data to be non-equidistant for the values o x. I found the program on the museum DVD and decided to revive it.

I have posted a document on my website (click here and select the link to the New quadratic Lagrangian Integration method). There is another link next to it to download a ZIP file containing the Excel file (with VBA code) I used to test the algorithm and compare it with Simpson's rule. The quadratic Lagrangian integration method does very well compared to Simpson's rule, especially with a good choice for the values of x. The document explains all that in more details.

Enjoy!

Namir

Edited: 20 July 2012, 9:38 a.m.

Namir, very nice read! I intend to spend some time with this article and reproduce your chart on page 3 to fully develop my understanding of it. I also particularly enjoyed the article on Shammas Polynomials, the refined CombSort Algorithm, and the new Square Root Algorithm. I have you bookmarked and will spend a delightful 3 or 4 evenings studying them at length. Thanks for the web site.

Les,

Thank you for your kind words. I hope you enjoy the new algorithms.

Namir