Re: Root finding needs higher accuracy

*To*: mathgroup at smc.vnet.net*Subject*: [mg123171] Re: Root finding needs higher accuracy*From*: "Harvey P. Dale" <hpd1 at nyu.edu>*Date*: Fri, 25 Nov 2011 04:56:08 -0500 (EST)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*References*: <201111241157.GAA29024@smc.vnet.net>

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

**References**:**Root finding needs higher accuracy***From:*HwB <hwborchers@googlemail.com>