I have a matrix that is 100M x 100M , where M stands for million. I need to read it into matlab to compute eigen values. I have a i7 Mac with 8GB. Is it sufficient or should I go for some solid state device with ~128GB or so..?
Also, all I need is just the product of eigenvalues of my 100M x 100M matrix. If there is a shortcut to compute the product directly without having to compute each and every eigen value, that is preferable.
If computing eigen values isn't feasible using matlab for the size of matrix I'm dealing with, please suggest a different package that can do it at least on a supercomputing (HPC) facility
Can SVD be used instead of eigen value computation to get the product of eigen values? Any SVD package that can speed up my computation?
thanks in advance!
100M x 100M full matrix is over 71 PETA bytes! No, I don't think you have enough memory (or time) to do this. Is your matrix sparse? If not you need to reformulate your problem.
The product of the eigenvalues of a matrix is equal to the determinant of the matrix. Assuming you can even calculate it, what do you plan to do with this (probably very inaccurate) determinant anyway?