       Re: Find smallest eigenvalues in mathematica

• To: mathgroup at smc.vnet.net
• Subject: [mg85598] Re: Find smallest eigenvalues in mathematica
• From: dh <dh at metrohm.ch>
• Date: Thu, 14 Feb 2008 06:29:49 -0500 (EST)
• References: <fp0ljo\$5mi\$1@smc.vnet.net>

```
Hi,

imagine that you subtract asome number from your eigenvalues so that all

Eigenvalues are negative. Then you can use Eigenvalues[..,1] to get the

smallest. This can be achieved by subtracting n IdentityMatrix from your

matrix, where n is larger than you largest positive eigenvalue.

Therefore, the following gives you the samllest eigenvalue:

n+Eigenvalues[m- n IdentityMatrix[dimension],1]

hope this helps, Daniel

thunk wrote:

> Eigenvalues[m, -k] gives the k that are smallest in absolute value,Here m is large sparse matrix. But I want to get the smallest eigenvalues,not in the meaning of absolute value,how can I achieve this aim directly,excluding the method that find the smallest eigenvalues in absolute value and select out the smallest values,for the method would waste many computational cost.How could we use Lanczos method according to Mathematica?

>

```

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