Re: Eigenvalues works very slow

• To: mathgroup at smc.vnet.net
• Subject: [mg128497] Re: Eigenvalues works very slow
• From: Sseziwa Mukasa <mukasa at gmail.com>
• Date: Thu, 25 Oct 2012 01:42:34 -0400 (EDT)
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```Does the other system use infinite precision?

You can get an approximation of the eigenvalues by converting to machine precision:

(Debug) In[1]:= d = 25;
q = Table[
Table[1/2*Sqrt[i + j + 1]*KroneckerDelta[Abs[i - j], 1], {j, 0,
d - 1}], {i, 0, d - 1}];
h0 = Table[
Table[(i + 1/2)*KroneckerDelta[i, j], {j, 0, d - 1}], {i, 0, d - 1}];
lambda = 1/2;
q4 = lambda*q.q.q.q;
Timing[N[Eigenvalues[q4 + h0]]][[1]]
Timing[Eigenvalues[N[q4 + h0]]][[1]]
(Debug) Out[6]= 18.6794
(Debug) Out[7]= 0.00085

On Oct 24, 2012, at 3:30 AM, jure lapajne wrote:

> Hello,
> I'm trying to calculate eigenvalues of different sized matrices (from 10x10 to 1000x1000) using mathematica's built-in function - Eigenvalues. For smaller matrices it works ok, but for larger matrices it's just too slow. I tried writing the code in another system and it finds
eigenvalues very quickly (in a second or two at most) even for big matrices. I'm not sure whether am I doing something wrong or is the speed difference really this big.
> My code (you only need to change d to change the size of matrix):
> d = 25;
> q = Table[Table[1/2*Sqrt[i + j + 1]*KroneckerDelta[Abs[i - j], 1], {j, 0, d-1}],{i, 0, d - 1}];
> h0 = Table[Table[(i + 1/2)*KroneckerDelta[i, j], {j, 0, d - 1}], {i, 0,d-1}];
> lambda = 1/2;
> q4 = lambda*q.q.q.q;
> N[Eigenvalues[q4 + h0]]
>
> Thanks for help.
>

```

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