mac@harris.cis.ksu.edu (Myron A. Calhoun) (10/03/89)
In article <1989Sep28.161516.10353@rpi.edu> wrf@mab.ecse.rpi.edu (Wm Randolph Franklin) writes: [many lines deleted] >You can work out how many Taylor terms it would take to get that >accuracy. Editorial: Taylor series are for wimps. I'm under the impression that in any given range which doesn't have singularity points, Chebyshev polynomials (of the first kind) can be used to "telescope" Taylor series of degree N down to degree N-1 while retaining the same maximum error (but this error may pop up in places where it wasn't present in the original--kinda like squeezing a balloon). The difference between N and N-1 is only ONE term (although for some common trig functions which have only even- or odd- powered terms, it may LOOK like two?); which seems rather "wimpy" to me. I can see that if I'm going to calculate a particular series a jillion times, one less calculation would be nice, but I don't see that as being particularly significant otherwise. Do other Chebyshev polynomials provide even better telescoping? [more lines deleted] --Myron. -- Myron A. Calhoun, PhD EE, W0PBV, (913) 532-6350 (work), 539-4448 (home). INTERNET: mac@ksuvax1.cis.ksu.edu BITNET: mac@ksuvax1.bitnet UUCP: ...{rutgers, texbell}!ksuvax1!harry!mac