Hi All,
I just posted, on my web site, the following article for a new variant for the Romberg method. The article actually looks at several variants and selects the best one.
Enjoy!!
Namir
Edited: 18 Apr 2012, 12:49 a.m.
New variant for the Romberg Integration Method

04182012, 12:48 AM
Hi All, I just posted, on my web site, the following article for a new variant for the Romberg method. The article actually looks at several variants and selects the best one. Enjoy!!
Namir Edited: 18 Apr 2012, 12:49 a.m.
04182012, 12:50 AM
Thanks. This should be intriguing
04182012, 05:17 AM
Using both the HP15c and Wolfram Alpha I get values that differ from yours for these examples: ln(x)/x integrate 1 to 100 = 10.60378
x in radians Nick
Edited: 18 Apr 2012, 5:27 a.m.
04182012, 07:16 AM
Nick, Thanks for the corrections. I n the case of the sin(x), I meant sin(x)/x. I posted the article with the corrected results.
Namir Edited: 18 Apr 2012, 7:29 a.m. after one or more responses were posted
04182012, 07:24 AM
Quote: The standard name for the sin(x)/x function is sinc(x), an abbreviation of sinus cardinalis (i.e.: cardinal sine). Regards from V.
04182012, 07:31 AM
Right you are! And I learned a new function name. Alpha Worlfram recognized the sinc(x) funcion!! :=)
04182012, 07:39 AM
So does the 34S :)
04182012, 07:47 AM
This brings back memories as the sinc function was one of the first things I plotted as a teenager on my newly acquired Sinclair ZX81 computer. Nick
04182012, 09:45 AM
Quote: I'm glad you did, I also learn new things each and every day.
About the sinc(x) function, it has many interesting properties and quirks but the one
but lo and behold, we unexpectedly find that
You might want to check this amazing fact by trying and computing said integrals I1, I2, ..., I8 using the 34S' extreme precision capabilities, it would be a fine test for any numerical integration procedure such as yours ! ... XD Best regards from V. 
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