Single- and Multiple-Vector Iterations
  M. Gu

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 $(m-1)/m$, where $m$ is the multiplicity of the eigenvalue.