Comment on "Spectral filters in quantum mechanics: a measurement theory perspective".
We criticize a paper by Vijay and Wyatt [Phys. Rev. E 63, 4351 (2000)], in which the authors suggest that energy levels computed, from the same set of matrix-vector products, with the filter diagonalization method (FDM) and the Fourier spectral analysis using the same Chebyshev correlation function are of comparable accuracy. We explain why the FDM is superior and demonstrate it numerically, using the same test matrix as that employed in the above paper. We also compare the FDM with the Lanczos method, another commonly used iterative technique for computing eigenvalues. We find that eigenvalues in a low-density region near the middle of the spectrum converge more quickly with the FDM, but that the Lanczos method requires fewer matrix-vector products to converge all the eigenvalues.
Mandelshtam
Vladimir A
VA
Carrington
Tucker
T