APMA 1170 - Homework 8
Professor George Em Karniadakis

Consider the $(n\times n)$ matrix ${\bf A}$ the entries of which are computed from

$$a_{ij} = \frac{ij}{(i+j)^2}.$$

• Compute the entire eigenspectrum using the Lanczos algorithm for $n=5, \, 10,$ and n=20 at different accuracy levels.