Re: A question regarding a hyperbolic geometric function
- To: mathgroup at smc.vnet.net
- Subject: [mg86423] Re: [mg86396] A question regarding a hyperbolic geometric function
- From: "Ali K. Ozdagli" <ozdagli at gmail.com>
- Date: Tue, 11 Mar 2008 02:57:07 -0500 (EST)
- References: <200803100704.CAA24775@smc.vnet.net>
Hi Bob and all, I originally figured this problem while I was working with a second order ODE of which solution involves Hypergeometric1F1. I have plugged the solution back to the ODE and it turned out that the equation is not satisfied for all values of the independent variable. I know the solution is correct as I have checked it both with Mathematica and another software. The mistake in the result becomes apparent when you check the accuracy and precision with Accuracy[] and Precision[]. For example, Hypergeometric1F1[-26.9, -20.1, 30000] gives 5.868090710725125*10^13007 However, if you check accuracy and precision of the result you get Accuracy[Hypergeometric1F1[-26.9, -20.1, 30000]] = -12991.8 (negative is bad!!!) Precision[Hypergeometric1F1[-26.9, -20.1, 30000]] = 15.9546 Where the latter is also the machine precision in Mathematica. This means that the results are precisely wrong although we want them to be roughly correct. :) Any ideas about this? Best, Ali On 3/10/08, Bob Hanlon <hanlonr at cox.net> wrote: > v1 = Hypergeometric1F1[-26.9, -20.1, 30000] > > 5.86809071072512533577549124209830605005026`\ > 15.954589770191005*^13007 > > Use exact values until evaluating the Hypergeometric1F1 with extended precision > > v2 = N[Hypergeometric1F1[-269/10, -201/10, 30000], 100] > > 5.86809071072500808515263985241332834422719\ > \ > 6477241041525402740155487068020893691436344\ > \ > 4849172908349727305685895816448516416585189\ > 1451997662`100.*^13007 > > Although even without extra precision v1 is very close to v2 > > (v1 - v2)/v2 > > 1.99810515261962031039159`2.2552081099371497\ > *^-14 > > > > Bob Hanlon > > > ---- "Ali K. Ozdagli" <ozdagli at gmail.com> wrote: > > Hi, > > > > I am working with Mathematica in order to solve an ordinary > > differential equation with several boundary conditions. It turned out > > that the solution is Kummer confluent hypergeometric function, > > HyperGeometric1F1[a,b,x]. My problem is that for the values of a, b > > and x I am interested in, e.g. a=-26.9, b=-20.1, x=300000, the > > numerical accuracy of Mathematica is very poor. > > > > Can somebody suggest me a way to improve the mathematical accuracy of > > HyperGeometric1F1? I prefer a quick and easy way but also appreciate > > any hard way. > > > > Best, > > > > Ali > > > > -- > > > > Ali K. Ozdagli > > Ph.D. Student in Economics > > at University of Chicago > > > > -- Ali K. Ozdagli Ph.D. Student in Economics at University of Chicago
- References:
- A question regarding a hyperbolic geometric function
- From: "Ali K. Ozdagli" <ozdagli@gmail.com>
- A question regarding a hyperbolic geometric function