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arnoldi method with Mathematica


Hi,

I am using Mathematica v5 for computation of large non-symmetric
tridiagonal matrices. I am trying to use the Eigenvalues[] function
with Arnoldi method, however, I got the following errors:

Eigenvalues::arm: 
   Method->Arnoldi can only be used for matrices of machine numbers.

Does anyone know how to get around this error? I needed precision
higher than the machine precision. Thank you in advance for the help.

*** A simple example of my code is given below.

(* this is ok, but please see below *)
In[1]:= sp = SparseArray[N[{{1,2,3},{3,2,1},{1,1,1}}]]

Out[1]= SparseArray[<9>, {3, 3}]

In[3]:= Eigenvalues[sp,1,Method->Arnoldi]

Out[3]= {5.}     <--- gives answer without error, but....if I specify
precision using SetPrecision I get error messages.

In[4]:= $MinPrecision = 20 $MachinePrecision

Out[4]= 319.092

In[8]:= spm = SetPrecision[ SparseArray[N[{{1,2,3},{3,2,1},{1,1,1}}]],
$MinPrecision]

Out[8]= SparseArray[<9>, {3, 3}]

In[9]:=  Eigenvalues[spm,1,Method->Arnoldi]

Eigenvalues::arm: 
   Method->Arnoldi can only be used for matrices of machine numbers.


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