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Re: Find all roots with FindRoot

  • To: mathgroup at smc.vnet.net
  • Subject: [mg126285] Re: Find all roots with FindRoot
  • From: Andrzej Kozlowski <akozlowski at gmail.com>
  • Date: Sun, 29 Apr 2012 02:07:01 -0400 (EDT)
  • Delivered-to: l-mathgroup@mail-archive0.wolfram.com
  • References: <25227796.28036.1334923020612.JavaMail.root@m06> <201204260928.FAA05588@smc.vnet.net> <201204280927.FAA00717@smc.vnet.net> <CALe_+=rU23zCn2XiYYBwUi8WcSh6m-hr4bXVAaoxszM-fBztdQ@mail.gmail.com>


On 28 Apr 2012, at 13:02, Mikael Anderson wrote:

> Actually I was using NSolve and was happy with that (see below). Then 
I happened to see the post on RootSerach and wanted to test it to see if 
I get the same results as NSolve. I got surprised that by increasing the 
range I did not get the same answer and hence posted the question.
>
> BTW Andrzej, do you see any advantage in using Reduce compared to 
NSolve?
>

In Mathematica version 7 NSolve could only solve algebraic equations and 
Reduce could also solve transcendental (analytic) ones as well as 
inequalities. In version 8 NSolve can solve the same kind of equations 
as Reduce (I think it actually calls on Reduce to solve non-algebraic 
equations so you are actually using Reduce) and it even takes the 
options WorkingPrecision->Infinity:

NSolve[x^2 - x + 1 == 0, x, WorkingPrecision -> Infinity]
{{x -> (-1)^(1/3)}, {x -> -(-1)^(2/3)}}

The differences, apart from the different form of output concerns 
solving inequalities (NSolve can't do that) and equations with symbolic 
parameters (NSolve can't do that but Solve can).

The reason why I used Reduced is that I still sometimes forget who much 
Solve and NSolve were upgraded in Mathemaitca 8.


Andrzej Kozlowski





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