Re: numerical, bessel
- To: mathgroup at smc.vnet.net
- Subject: [mg55258] Re: numerical, bessel
- From: Paul Abbott <paul at physics.uwa.edu.au>
- Date: Thu, 17 Mar 2005 03:30:59 -0500 (EST)
- Organization: The University of Western Australia
- References: <d193ob$nmg$1@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
In article <d193ob$nmg$1 at smc.vnet.net>,
Richard Fateman <fateman at cs.berkeley.edu> wrote:
> << NumericalMath`BesselZeros`
> BesselJZeros[0, {17, 19}, WorkingPrecision -> 30]
>
> works, but
>
> BesselJZeros[0, {17, 19}, AccuracyGoal -> 30]
>
> just returns unevaluated.
Not in 5.1.
> The documentation for NumericalMath`BesselZeros` claims that
> AccuracyGoal, as well as WorkingPrecision is an option. Apparently not.
> version 5.0
In 5.1 one gets the following warning:
AccuracyGoal -> 30 is not a valid value, or is larger than
WorkingPrecision -> MachinePrecision, computation may not be able to
achieve desired accuracy.
One can argue the case whether setting AccuracyGoal -> 30 should cause
the WorkingPrecision to be increased automatically. However, a
combination of the two options together yields the desired result and is
consistent with the documentation:
BesselJZeros[0, {17, 19}, AccuracyGoal -> 30, WorkingPrecision -> 40]
I wrote a naive RootsInRange function that works with arbitrary
functions:
Needs["Utilities`FilterOptions`"]
RootsInRange[d_, {l_, lmin_, lmax_}, opts___] :=
Module[{s, p, x, f = Function[l, Evaluate[d]]},
s = Plot[f[l], {l, lmin, lmax}, Compiled -> False,
Evaluate[FilterOptions[Plot, opts]]];
p = Cases[s, Line[{x__}] -> x, Infinity];
p = Map[First, Select[Split[p, Sign[Last[#2]] == -Sign[Last[#1]]&],
Length[#1] == 2 & ], {2}];
Apply[FindRoot[f[l] == 0, {l, ##1},
Evaluate[FilterOptions[FindRoot, opts]]] &, p, {1}]
]
Entering
RootsInRange[BesselJ[0, x], {x, 50, 60},
AccuracyGoal -> 30, WorkingPrecision -> 40]
gives the same answer as the invocation of BesselJZeros above.
Alternatively, Ted Ersek's RootSearch package at
http://library.wolfram.com/infocenter/MathSource/4482/
appears to be robust for such computations.
Cheers,
Paul
--
Paul Abbott Phone: +61 8 6488 2734
School of Physics, M013 Fax: +61 8 6488 1014
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