MathGroup Archive 2011

[Date Index] [Thread Index] [Author Index]

Search the Archive

Re: Root finding needs higher accuracy


Hans:

	The option you need is WorkingPrecision.

FindRoot[Log[x]+x^2/(2 Exp[1])-2
x/Sqrt[Exp[1]]+1==0,{x,1},WorkingPrecision->50]

	Best,

	Harvey


-----Original Message-----
From: HwB [mailto:hwborchers at googlemail.com]
Sent: Thursday, November 24, 2011 6:57 AM
To: mathgroup at smc.vnet.net
Subject: [mg123171] Root finding needs higher accuracy

I would like to numerically find the root of the following function with
up to 20 digits.

    f12[x_] := Log[x] + x^2 / (2 Exp[1]) - 2 x / Sqrt[Exp[1]] + 1

This problem is known to be difficult for solvers in double precision
arithmetics. I thought it should be easy with Mathematica, but the
following attempts were not successful.

    SetPrecision[
        x /. FindRoot[f12[x], {x, 1.0, 3.4}, Method -> "Brent",
                 AccuracyGoal -> Infinity, PrecisionGoal -> 20], 16]
    # 1.648732212532746
    SetPrecision[
        x /. FindRoot[f12[x], {x, 1.0, 3.4}, Method -> "Secant",
                 AccuracyGoal -> Infinity, PrecisionGoal -> 20], 16]
    # 1.648710202030051

The true root obviously is Sqrt[Exp[1]]//N = 1.648721270700128...

The symbolic solver explicitely says it cannot solve this expression.
What do I need to do to get a much more exact result out of Mathematica?

Many thanks, Hans Werner




  • Prev by Date: Re: Root finding needs higher accuracy
  • Next by Date: Re: Root finding needs higher accuracy
  • Previous by thread: Root finding needs higher accuracy
  • Next by thread: Re: Root finding needs higher accuracy