I'm trying to efficiently calculate the eigenvalues for this matrix. It looks like this:

http://www.math.pitt.edu/~sussmanm/2071Spring08/lab06/img2.png

It's diagonalized by the DST matrix in a similar way that a circulant matrix is diagonalized by the DFT. In the case of the circulant matrix, you can take the DFT of the first column to get the eigenvalues. I'm trying to do a similar thing for the second difference matrix using the DST function in matlab. The best I can get are half the eignvalues by taking the dst of the middle column. Anyone have any ideas how I can do this (Without explicitly forming the DST matrices and second difference matrix)? Thanks.