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Is there a lowest Eigenvalues function around?



I have to find the eigenvalues of very large matrices, ie 1024x1024 up
to over 10000x10000 .  I run out of memory when trying to do more than
about 1600x1600 .  I know there are algorithms to find the lowest or
highest eigenvalues of a matrix, but the Mathematica function
Eigenvalues[] finds all of them.  

Does anyone know if there is an implementation of a lowest-eigenvalues
function anywhere?  I have looked aroung at www.wolfram.com but didn't
find anything.

Also, I wonder about memory usage in storing matrices.  If a matrix is
sparse, does it require less memory to store and manipulate than a
not-sparse matrix?  Does a matrix with only real values require less
memory than a complex matrix?


Thanks.
-- 
_______________________
Christopher R. Carlen
crobc@epix.net          <--- Reply here, please. carlenc@cs.moravian.edu
My OS is Linux v2



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