**``Dir''**- is direct application, where we multiply with and solve with .
**``SI''**- is shift and invert, which solves systems for and multiplies with . This gives the ability to compute a wider choice of eigenvalues in fewer iterations.
**``Prec''**- means application with a preconditioner, for instance, a sparse approximate factorization. This needs less space than shift and invert, but most often it also needs a larger number of matrix-vector multiplies.

Susan Blackford 2000-11-20