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Re: Documentation of Eigenvalues[], Eigensystem[]

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  • Subject: [mg114046] Re: Documentation of Eigenvalues[], Eigensystem[]
  • From: Murray Eisenberg <murray at math.umass.edu>
  • Date: Mon, 22 Nov 2010 07:35:51 -0500 (EST)

This is definitely a gap in the documentation.

To find out that Eigenvalues has a Method option is easy, though:

    Options[Eigenvalues]
{Cubics -> False, Method -> Automatic, Quartics -> False}

What is difficult (impossible), however, is to find out for a Method 
option -- and a number of functions have it -- is what the possible 
settings are.

In any case, the reference page for Eigenvalues is clearly incomplete.

Of course one should try to avoid the Method option where possible, 
allowing Mathematica to choose (via the default Automatic setting for 
Method), the "best" method. This is one of the "big" design principles 
of the system: automation.

On 11/20/2010 6:23 PM, Michael Weyrauch wrote:
> Hello
>
>      it appears that the documentation of some "classic" functions
> like Eigenvalues[] and Eigensystem[] is rather incomplete in
> Mathematica 8 (and 7 and 6). Under the Options section one only finds
> the options Cubics and Quartics.
>
> In one example given in "Possible issues" section
> one realizes that there is also a "Method" option with rather obscurely
> defined suboptions like "Shift". From the Mathematica 5.2 docs
> (suposedly outdated) I also know that e.g. the following works (and
> still works in 8)
>
> Eigenvalues[matrix, 2, Method->{"Arnoldi", StartingVector->  vector}]
>
> and it is indeed sometimes very time efficient to be able to give
> a starting vector to the Arnoldi iteration procedure. Unfortunately all
> these possibilities are not documented in more recent
> versions of Mathematica, which I find very odd given that e.g. rather
> extremely special functions like NVCCCompiler[] are documented with an
> extensive list of even the most outlandish options (I guess).
>
> Does anybody know of a comprehensive list of "Options" available
> for some "classic" functions like Eigenvalues etc.? (For the Frontend we
> even have an "Options inspector". Maybe there is also one for other
> functions??)
>
> Michael Weyrauch
>

-- 
Murray Eisenberg                     murray at math.umass.edu
Mathematics & Statistics Dept.
Lederle Graduate Research Tower      phone 413 549-1020 (H)
University of Massachusetts                413 545-2859 (W)
710 North Pleasant Street            fax   413 545-1801
Amherst, MA 01003-9305


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