I am looking mainly for implementations but also for theoretical algorithms to compute gaps between smallest positive eigenvalues of symmetric, singular matrix or real numbers.
To be precise, I want to find index n of the eigenvalue such that between $\lambda_n$ and $\lambda_{n+1}$ there is the largest gap (I assume that eigenvalues are sorted).
The matrix I am dealing with is huge, so I am allowed to use only sparse representation. I cannot store all the zero entries due to memory constraints.
Can you recommend any software which can compute it to me and uses sparse matrix representations?
Maybe you know some papers with algorithms solving this problem.
Thanks in advance!
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