My question is related to this one. I am looking for the eigenvalues and eigenvectors of a square, symmetric, real Toeplitz matrix of order N where N is large.
There are some references in the above link but they seem to be pretty high level. Any advice to be had out there?
This business is related to the generation of realizations of correlated random variables. The problem is that in order to generate a realization of $M$ correlated random variables, I have a symmetric, real Toeplitz matrix of order $M^2$ which must be decomposed. This quickly fills up memory. But the all of the information of the matrix is stored in the first row/column. It would be very useful to be able to just know the eigenvalues and eigenvectors, or at least have a good approximation for them.
