Re: Using FindRoot on an equation involving Log terms

*To*: mathgroup at smc.vnet.net*Subject*: [mg115720] Re: Using FindRoot on an equation involving Log terms*From*: Gabriel Landi <gtlandi at gmail.com>*Date*: Wed, 19 Jan 2011 05:26:20 -0500 (EST)

Hey Andrew, The problem is likely the direction it uses to begin the search. x = 0.655 is a minimum. If you give a initial value above that it finds your root. If you give a initial value below that it will go the other way which eventually diverges when x approaches zero. You can take a better look using the following two lines of code: << Optimization`UnconstrainedProblems` FindRootPlot[expr, {x, 0.6}, PlotRange -> {{0, 1}, {-100, 100}}] (The output graph comes out bugged but you can still see what you need to see: the steps it took). The colors are explained in http://reference.wolfram.com/mathematica/tutorial/UnconstrainedOptimizationPlottingSearchData.html By the way, FindInstance works: FindInstance[expr == 0, x, Reals] // N Cheers, Gabriel On Tue, Jan 18, 2011 at 8:51 AM, Andrew DeYoung <adeyoung at andrew.cmu.edu>wrote: > Hi, > > I am trying to find the root of a certain expression in Mathematica > version 7: > > expr = 110.52499999999998 + (300. - 135.52499999999998/(1 - x)) (1 - > x) - 300. x - 135.52499999999998 Log[1 - x] + 135.52499999999998 > Log[x] > > It appears to plot fine, for example using Plot[expr, {x, 0, 1}]. The > plot shows that there should be a root at about x=0.85. However, when > I try to find this root, using for example the following: > > FindRoot[expr, {x, 0.5}] > > I get an error message: > > "FindRoot::lstol: The line search decreased the step size to within > tolerance specified by AccuracyGoal and PrecisionGoal but was unable > to find a sufficient decrease in the merit function. You may need > more than MachinePrecision digits of working precision to meet these > tolerances." > > and it prints a seemingly incorrect (according to the qualitative form > of the plot) result: {x -> 0.344678}. Only if I use for example > > FindRoot[expr, {x, 0.7}] > > do I get the seemingly "correct" root: {x -> 0.849823}. > > Can you help me see why the FindRoot is getting stuck at {x -> > 0.344678} when I use starting values far away from 0.7 or 0.8? I will > ultimately want to find the roots of many similar functions, which may > have more than one "actual" root, so it would be helpful if I could > see why FindRoot[expr, {x, 0.5}] does not give {x -> 0.849823}. (also > when I tried NSolve[expr==0,x], Mathematica will not solve it.) > > Thank you, > > Andrew DeYoung > Carnegie Mellon University >