We now consider some of the issues and tradeoffs that should be considered when selecting the block size. For this discussion we assume that comparisons are made using a fixed maximum dimension for the subspace.
As the block size increases, the length of the Arnoldi reduction 
decreases. Since the degree of the largest power of 
in the corresponding
Krylov space is 
smaller block sizes allow polynomials of larger
degree to be applied.
The down side to an unblocked method is that it cannot compute multiple copies
of an eigenvalue of unless the reduction already well-approximates some
of the associated eigenvectors. For example, the first Ritz pair should give a
residual of 
or smaller relative to the norm of
before the second copy emerges.
One of the benefits of block methods is that they are more reliable for computing approximations to the clustered and/or multiple eigenvalues using a relatively large convergence criterion. Note that the block size used may be varied during each restart.