Block methods are used for two major reasons. The first one is to aid in reliably determining multiple and/or clustered eigenvalues. Although  indicates that an unblocked Arnoldi method coupled with an appropriate deflation strategy may be used to compute multiple and/or clustered eigenvalues, a relatively small convergence tolerance is required to reliably compute clustered eigenvalues. Many problems do not require this much accuracy, and such a criterion can result in unnecessary computation. The second reason for using a block formulation is related to computational efficiency. Often, when a matrix-vector product with is very costly, it is possible to compute the action of on several vectors at once with roughly the same cost as computing a single matrix-vector product. This can happen, for example, when the matrix is so large that it must be retrieved from disk each time a matrix-vector product is performed. In this situation, a block method may have considerable advantages.
The performance tradeoffs of block methods and potential improvements to deflation techniques are under investigation.