New variant for the Romberg Integration Method  Printable Version + HP Forums (https://archived.hpcalc.org/museumforum) + Forum: HP Museum Forums (https://archived.hpcalc.org/museumforum/forum1.html) + Forum: Old HP Forum Archives (https://archived.hpcalc.org/museumforum/forum2.html) + Thread: New variant for the Romberg Integration Method (/thread218266.html) 
New variant for the Romberg Integration Method  Namir  04182012 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.
Re: New variant for the Romberg Integration Method  Matt Agajanian  04182012 Thanks. This should be intriguing
Re: New variant for the Romberg Integration Method  Nick_S  04182012 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.
Re: New variant for the Romberg Integration Method  Namir  04182012 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
Re: New variant for the Romberg Integration Method  Valentin Albillo  04182012 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.
Re: New variant for the Romberg Integration Method  Namir  04182012 Right you are! And I learned a new function name. Alpha Worlfram recognized the sinc(x) funcion!!
:=)
Re: New variant for the Romberg Integration Method  Paul Dale  04182012 So does the 34S :)
Re: New variant for the Romberg Integration Method  Nick_S  04182012 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
Re: New variant for the Romberg Integration Method  Valentin Albillo  04182012 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.
