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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.