Re: Bad Precision output for SphericaBesselY and BesselY
- To: mathgroup at smc.vnet.net
- Subject: [mg123151] Re: Bad Precision output for SphericaBesselY and BesselY
- From: Antonio Alvaro Ranha Neves <aneves at gmail.com>
- Date: Thu, 24 Nov 2011 07:00:00 -0500 (EST)
- Delivered-to: l-mathgroup@mail-archive0.wolfram.com
- References: <jafud8$rrr$1@smc.vnet.net>
- Reply-to: comp.soft-sys.math.mathematica at googlegroups.com
Thank you Oleksander, Peter, Oliver, and Richard for the reply.
@Oleksander
Why is Rationalize[120.3] better than SetPrecision[120.3, Infinity]?
Each command gives me a rational output,
1203/10
And
8465359924572979/70368744177664
Respectivaly.
I used 120.3 as an example, but my actual number is an irrational number with a high precision (output of a findroot)
@Peter
I really liked the FindRoot solution to the problem. It inspired me to write,
ListMap=ParallelTable[Replace[p,FindRoot[Precision[BesselY[n+1/2,SetPrecision[x,p]]]==90,{p,90},Evaluated->False]],{x,100},{n,100}];
ListPlot3D[ListMap,Mesh->None,ColorFunction->"SouthwestColors"]
Maybe this will shed some light on how the precision is affected by BesselY[n+1/2,x] algorithm. As one can see, when x is approximately n the required precision is maximum, and when x>n there are some =93instabilities=94.