EigenSolvers
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 maximum and minimum eigenvalues using the Inverse Shifted Power Method for n=5, 10 and 20 at different accuracy levels (adaptivity is optional).
• Compute the entire eigenspectrum using the Lanczos algorithm for n=5, 10 and 20 at different accuracy levels.