Services & Resources / Wolfram Forums / MathGroup Archive
-----

MathGroup Archive 2008

[Date Index] [Thread Index] [Author Index]

Search the Archive

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?

> 




  • Prev by Date: Re: eliminate all the occurrences of "theta ->" and "lambda ->"
  • Next by Date: Re: Automatic Differentiation in Mathematica
  • Previous by thread: Re: eliminate all the occurrences of "theta ->" and "lambda ->"
  • Next by thread: Re: Find smallest eigenvalues in mathematica