This thesis addresses the parallelization of restarted Krylov methods
for eigenproblems and singular value (SVD) problems.  These methods
are iterative in nature and are appropriate for finding a few
eigenvalues or singular values from sparse problems.  In this kind
of methods, the part with the higher cost is the ortogonalization
procedure.  Therefore this procedure has received special attention
in this thesis.  New algorithms have been proposed and validated
in order to improve its parallel performance.

The implementation has been made in the framework provided by the
SLEPc library.  This library provides an object oriented interface
for iterative eigensolvers or SVD solvers.  SLEPc is based on PETSc,
which provides parallel implementations of lineal solvers,
preconditioners, sparse matrices and vectors.  Both libraries are
optimized for distributed memory parallel computers with very large
sparse matrices.

This implementation includes the following eigenvalue methods:
explicitly restarted Arnoldi, explicitly restarted Lanczos (with
semiorthogonal variants) and Krylov-Schur (equivalent to implicit
restart) for non-Hermitian and Hermitian (also known as thick restart
Lanczos) matrices.  These methods share a common interface, which
enables an easy comparison between them, feature that is not available
in any other implementation.  The same techniques employed for
eigenproblems have been adapted to the SVD Golub-Kahan-Lanczos
methods with explicit and thick restart, which have no previous
implementation with message-passing parallelism.

Each one of the methods has been validated through a battery of
tests with matrices from a variety of applications.  Parallel
performance has been measured in cluster computers, showing good
scalability even with a large number of processors, and obtaining
competitive performance with current state of the art software.