arnoldi method with Mathematica

• To: mathgroup at smc.vnet.net
• Subject: [mg45951] arnoldi method with Mathematica
• From: hweekuan at yahoo.com (Hwee Kuan)
• Date: Fri, 30 Jan 2004 04:16:57 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

```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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