  A deflated and restarted Lanczos algorithm to solve hermitian linear systems,
and at the same time compute eigenvalues and eigenvectors for application to
multiple right-hand sides, is described. For the first right-hand side,
eigenvectors with small eigenvalues are computed while simultaneously solving
the linear system. Two versions of this algorithm are given. The first is
called Lan-DR and is based on conjugate gradient (CG) implementation of the
Lanczos algorithm. This version will be optimal for the hermitian positive
definite case. The second version is called MinRes-DR and is based on the
minimum residual (MinRes) implementation of Lanczos algorithm. This version is
optimal for indefinite hermitian systems where the CG algorithm is subject to
instabilities. For additional right-hand sides, we project over the calculated
eigenvectors to speed up convergence. The algorithms used for subsequent
right-hand sides are called D-CG and D-MinRes respectively. After some
introductory examples are given, we show tests for the case of Wilson fermions
at kappa critical. A considerable speed up in the convergence is observed
compared to unmodified CG and MinRes.
