I want to compute the spectrum (all the eigenvalues) of a large sparse matrix (hundreds of thousands of rows). This is hard.I am willing to settle for an approximation. Are there approximation methods to do this?While I hope for a general answer to this question I would also be satisfied with an answer in the following specific case. My matrix is a Normalized Laplacian of a large graph. Eigenvalues will be between 0 and 2 with a large number of them clustered around 1.
Approximate spectrum of a large matrix
linear algebra;numerics;eigensystem;graph theory;approximation algorithms