Now we discuss the pros and cons of the methods for Hermitian eigenproblems from Chapter 4 as applied to , , or . We note that the special structure of may be exploited to make Lanczos more efficient, as described in §6.3.3 below.
For simplicity, we let denote any one of the above three Hermitian matrices in the discussion below. The basic tradeoffs from Table 4.1 remain true; the choice of method depends on the following:
What differs from Chapter 4 is how the above decisions depend on the choice of .