The single- and multiple-vector iteration methods for the
Hermitian eigenproblem in §4.3 can
also be used to solve the NHEP, in
many cases with similar convergence properties. Although
these methods are in general not as competitive as the other
methods to be covered in later sections, they are a good
choice for those who only want to find a few extreme
eigenvalues with a very simple method.
The Rayleigh quotient iteration (RQI) will have an ultimately quadratic rate of
convergence, which is slower than the cubic rate for the Hermitian case.
When converging to a defective eigenvalue it has a slow linear
rate , where
is the multiplicity of the eigenvalue.