PI
in [Matlab]
|
From: eddgarms Edgar on 9 Jun 2010 12:06 Hello I would be very gratefull if someone could help me solve the following problem: How to compare the speed of convergence of two development pi series in Matlab ? (if possible with a concrete example) Thank you all. Yours sincerely, Edgar
From: Walter Roberson on 9 Jun 2010 12:19 eddgarms Edgar wrote: > I would be very gratefull if someone could help me solve the following > problem: > How to compare the speed of convergence of two development pi series in > Matlab ? > (if possible with a concrete example) I'm not sure what a "development" series is, but to compare the speed of convergence of two series you need to figure out how many steps are needed to be _certain_ that you have at least one more bit (or one more digit) of accuracy in the answer. "After N steps, we will have calculated N/2 digits" or "After N steps, we will have calculated sqrt(N) digits" or "After N steps, we will have calculated 2*N digits" or whatever you work it out to be. If you write a program that attempts to determine experimentally how quickly you arrive at the answer, be sure not to include accidental convergence. For example, one calculation might go from 3.14 to 3.1414 and then to 3.1409 with the 3.1414 actually being an "overshoot" in the convergence process, and the 3.1409 being a correction back and later terms contributing positive values that eventually increase it to 3.1415<something> . You should necessarily count a digit as being right the _first_ time it appears to be right: further calculation might move away from it. A digit is "correct" when the remaining terms are _provably_ not able to change the digit -- a determination that requires looking at the value and stability of the _next_ digit, because of rounding.
From: Walter Roberson on 9 Jun 2010 14:22 Walter Roberson wrote: > You should necessarily count a digit as being right > the _first_ time it appears to be right: further calculation might move > away from it. Sorry, that should be "You should _not_ necessarily [...]"
|
Pages: 1 Prev: Requring matlab code to study mobility model Next: parsing a large blob of ascii data |