Re: Possible bug in NSolve[equation, variable, precission]

*To*: mathgroup at smc.vnet.net*Subject*: [mg74342] Re: Possible bug in NSolve[equation, variable, precission]*From*: "Julian Aguirre" <julian.aguirre at ehu.es>*Date*: Mon, 19 Mar 2007 02:03:46 -0500 (EST)*References*: <etg4m9$ioi$1@smc.vnet.net><etijrq$j05$1@smc.vnet.net>

On 18 mar, 06:48, "dimitris" <dimmec... at yahoo.com> wrote: > Why use NSolve in your equation? Use Solve instead! > [Mathematica code removed] > Regards > Dimitris Somehow I thought NSolve was appropriate, since the polynomials in my application are always irreducible, of moderate to large degree, and with large integer or rational coefficients. I have followed your suggestion, and I have found: 1) My code runs faster 2) Some problems related to different but very close roots have dissapeared 3) Because of this I need less precission in the calculations. So, thanks a lot. But I still I am puzzeld as to why NSolve chokes on that particular polynomial. Juli=E1n > Julian Aguirre wrote: > > Dear group, > > > Mathematica 5.2 chokes solving numerically a polynomial equation. > > > In[1] := $Version > > Out[1]= 5.2 for Mac OS X (64 bit) (June 20, 2005) > > > In[2]:= poly=171142046150220198693105489-16023210221608713837587916 > > x-2020825892011586434364754 x^2+190894692033395024364972 > > x^3+6039743423966949379761 x^4-568929229651998950400 > > x^5-470066550477520896 x^6+2821109907456 x^7; > > > In[3]:= poly2=Expand[poly/9]; > > > In[4]:= NSolve[poly==0,x] > > Out[4]= {-1211.83, -13.0015, -13.0014, 11.923, 12.0809, 12.2509, > > 167826.} > > > (* Up to this moment, everything is O.K. But *) > > > In[5]:= NSolve[poly==0,x,20] > > Out[5]= $Aborted (* after a loooong time *) > > > (* However, the following works as expected*) > > > In[6]:= x/.NSolve[poly2==0,x,20] > > Out[6]= {-1211.8267955098487289, -13.001455891126, -13.001441554521, > > 11.92303189062617, 12.08089051352363, 12.25087466630727, > > 167826.26017849924816} > > > Let me say that I have used Mathematica to solve thousands (probably > > millions) of equations like the one above. There must be some magic in > > the coefficients!