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RootSearch options

  • To: mathgroup at
  • Subject: [mg65376] RootSearch options
  • From: ted.ersek at
  • Date: Wed, 29 Mar 2006 06:34:15 -0500 (EST)
  • Sender: owner-wri-mathgroup at

I wrote the RootSearch package on MathSource.
David W. Cantrell noted that with the default options
RootSearch doesn't find all roots in the specified
interval in the following example.

Below I give three ways to get all the roots using RootSearch.


   Cot[x] == x/a - a/(4*x), {x, 10^-6, 50},
   RootTest->(True&), InitialSamples->500

   Cot[x] == x/a - a/(4*x), {x, 10^-6, 50},
   RootTest->((Abs[#2]<1.0*^-7)&), InitialSamples->500

  RootSearch[Cot[x] == x/a - a/(4*x), {x, 10^-6, 50},
    InitialPrecision->30, InitialSamples->500
  ] ;

With the a higher setting for InitialSamples
RootSearch looks harder. Some functions are very time consuming
to evaluate. In such cases we have a trade off between making
sure all roots are found, and the time it takes to find the roots.

With the above settings for the RootTest option you have a greater
risk that some of the "roots found" are actually points very close
to a discontinuity where (lhs-rhs) changes sign. The RootTest option
ensures "roots found" where Abs[lhs-rhs] is "too large" are thrown

Sorry for the delay responding. I don't have a lot of time for
MathGroup correspondence.

  Ted Ersek

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